InforLorV4, Main, Exploration, bibRecord, 000104

Silhouette of a random polytope

Identifieur interne : 000104 ( Main/Exploration ); précédent : 000103; suivant : 000105

Silhouette of a random polytope

Auteurs : Marc Glisse [France] ; Sylvain Lazard [France] ; Julien Michel [France] ; Marc Pouget [France]

Source :

Journal of Computational Geometry [ 1920-180X ] ; 2016.

RBID : Hal:hal-01289699

Abstract

We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\Theta(\sqrt{n})$.

Url:

https://hal.inria.fr/hal-01289699

Affiliations:

Links toward previous steps (curation, corpus...)

to stream Hal, to step Corpus: 004565
to stream Hal, to step Curation: 004565
to stream Hal, to step Checkpoint: 000109
to stream Main, to step Merge: 000157
to stream Main, to step Curation: 000104

Le document en format XML

<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Silhouette of a random polytope</title>
<author><name sortKey="Glisse, Marc" sort="Glisse, Marc" uniqKey="Glisse M" first="Marc" last="Glisse">Marc Glisse</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-56048" status="VALID"><idno type="RNSR">200318408A</idno>
<orgName>Geometric computing</orgName>
<orgName type="acronym">GEOMETRICA</orgName>
<desc><address><addrLine>2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) / Bât Alan Turing, Campus de l'Ecole Polytechnique, 1 rue Honoré d'Estienne d'orves, 91120 Palaiseau (France)</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www-sop.inria.fr/geometrica/</ref>
</desc>
<listRelation><relation active="#struct-34586" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-118511" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-34586" type="direct"><org type="laboratory" xml:id="struct-34586" status="VALID"><idno type="RNSR">198318250R</idno>
<orgName>Inria Sophia Antipolis - Méditerranée </orgName>
<orgName type="acronym">CRISAM</orgName>
<desc><address><addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/sophia/</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-118511" type="direct"><org type="laboratory" xml:id="struct-118511" status="VALID"><idno type="RNSR">200818248E</idno>
<orgName>INRIA Saclay - Ile de France</orgName>
<desc><address><addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/saclay</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205129" status="VALID"><idno type="RNSR">200518305E</idno>
<orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName>
<orgName type="acronym">VEGAS</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/vegas</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Michel, Julien" sort="Michel, Julien" uniqKey="Michel J" first="Julien" last="Michel">Julien Michel</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-183436" status="VALID"><orgName>Laboratoire de Mathématiques et Applications</orgName>
<orgName type="acronym">LMA-Poitiers</orgName>
<desc><address><addrLine>Téléport 2 - BP 30179 Boulevard Marie et Pierre Curie 86962 Futuroscope Chasseneuil Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www-math.univ-poitiers.fr/</ref>
</desc>
<listRelation><relation active="#struct-54493" type="direct"></relation>
<relation name="UMR7348" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-54493" type="direct"><org type="institution" xml:id="struct-54493" status="VALID"><orgName>Université de Poitiers</orgName>
<desc><address><addrLine>15, rue de l'Hôtel Dieu - 86034 Poitiers Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-poitiers.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7348" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Poitiers</settlement>
<region type="old region" nuts="2">Poitou-Charentes</region>
<region type="region" nuts="2">Nouvelle-Aquitaine</region>
</placeName>
<orgName type="university">Université de Poitiers</orgName>
</affiliation>
</author>
<author><name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205129" status="VALID"><idno type="RNSR">200518305E</idno>
<orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName>
<orgName type="acronym">VEGAS</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/vegas</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01289699</idno>
<idno type="halId">hal-01289699</idno>
<idno type="halUri">https://hal.inria.fr/hal-01289699</idno>
<idno type="url">https://hal.inria.fr/hal-01289699</idno>
<date when="2016">2016</date>
<idno type="wicri:Area/Hal/Corpus">004565</idno>
<idno type="wicri:Area/Hal/Curation">004565</idno>
<idno type="wicri:Area/Hal/Checkpoint">000109</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000109</idno>
<idno type="wicri:doubleKey">1920-180X:2016:Glisse M:silhouette:of:a</idno>
<idno type="wicri:Area/Main/Merge">000157</idno>
<idno type="wicri:Area/Main/Curation">000104</idno>
<idno type="wicri:Area/Main/Exploration">000104</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Silhouette of a random polytope</title>
<author><name sortKey="Glisse, Marc" sort="Glisse, Marc" uniqKey="Glisse M" first="Marc" last="Glisse">Marc Glisse</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-56048" status="VALID"><idno type="RNSR">200318408A</idno>
<orgName>Geometric computing</orgName>
<orgName type="acronym">GEOMETRICA</orgName>
<desc><address><addrLine>2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) / Bât Alan Turing, Campus de l'Ecole Polytechnique, 1 rue Honoré d'Estienne d'orves, 91120 Palaiseau (France)</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www-sop.inria.fr/geometrica/</ref>
</desc>
<listRelation><relation active="#struct-34586" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-118511" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-34586" type="direct"><org type="laboratory" xml:id="struct-34586" status="VALID"><idno type="RNSR">198318250R</idno>
<orgName>Inria Sophia Antipolis - Méditerranée </orgName>
<orgName type="acronym">CRISAM</orgName>
<desc><address><addrLine>2004 route des Lucioles BP 93 06902 Sophia Antipolis</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/sophia/</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-118511" type="direct"><org type="laboratory" xml:id="struct-118511" status="VALID"><idno type="RNSR">200818248E</idno>
<orgName>INRIA Saclay - Ile de France</orgName>
<desc><address><addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/centre/saclay</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
</affiliation>
</author>
<author><name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205129" status="VALID"><idno type="RNSR">200518305E</idno>
<orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName>
<orgName type="acronym">VEGAS</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/vegas</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
<author><name sortKey="Michel, Julien" sort="Michel, Julien" uniqKey="Michel J" first="Julien" last="Michel">Julien Michel</name>
<affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-183436" status="VALID"><orgName>Laboratoire de Mathématiques et Applications</orgName>
<orgName type="acronym">LMA-Poitiers</orgName>
<desc><address><addrLine>Téléport 2 - BP 30179 Boulevard Marie et Pierre Curie 86962 Futuroscope Chasseneuil Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www-math.univ-poitiers.fr/</ref>
</desc>
<listRelation><relation active="#struct-54493" type="direct"></relation>
<relation name="UMR7348" active="#struct-441569" type="direct"></relation>
</listRelation>
<tutelles><tutelle active="#struct-54493" type="direct"><org type="institution" xml:id="struct-54493" status="VALID"><orgName>Université de Poitiers</orgName>
<desc><address><addrLine>15, rue de l'Hôtel Dieu - 86034 Poitiers Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-poitiers.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7348" active="#struct-441569" type="direct"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Poitiers</settlement>
<region type="old region" nuts="2">Poitou-Charentes</region>
<region type="region" nuts="2">Nouvelle-Aquitaine</region>
</placeName>
<orgName type="university">Université de Poitiers</orgName>
</affiliation>
</author>
<author><name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-205129" status="VALID"><idno type="RNSR">200518305E</idno>
<orgName>Effective Geometric Algorithms for Surfaces and Visibility</orgName>
<orgName type="acronym">VEGAS</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/equipes/vegas</ref>
</desc>
<listRelation><relation active="#struct-129671" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-423083" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-129671" type="direct"><org type="laboratory" xml:id="struct-129671" status="VALID"><idno type="RNSR">198618246Y</idno>
<orgName>INRIA Nancy - Grand Est</orgName>
<desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/nancy</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-423083" type="direct"><org type="department" xml:id="struct-423083" status="VALID"><orgName>Department of Algorithms, Computation, Image and Geometry</orgName>
<orgName type="acronym">LORIA - ALGO</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/algorithmics</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
<series><title level="j">Journal of Computational Geometry</title>
<idno type="ISSN">1920-180X</idno>
<imprint><date type="datePub">2016</date>
</imprint>
</series>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass></textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">We consider random polytopes defined as the convex hull of a Poisson point process on a sphere in $\R^3$ such that its average number of points is $n$. We show that the expectation over all such random polytopes of the maximum size of their silhouettes viewed from infinity is $\Theta(\sqrt{n})$.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
<li>Nouvelle-Aquitaine</li>
<li>Poitou-Charentes</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
<li>Poitiers</li>
</settlement>
<orgName><li>Université de Lorraine</li>
<li>Université de Poitiers</li>
</orgName>
</list>
<tree><country name="France"><noRegion><name sortKey="Glisse, Marc" sort="Glisse, Marc" uniqKey="Glisse M" first="Marc" last="Glisse">Marc Glisse</name>
</noRegion>
<name sortKey="Lazard, Sylvain" sort="Lazard, Sylvain" uniqKey="Lazard S" first="Sylvain" last="Lazard">Sylvain Lazard</name>
<name sortKey="Michel, Julien" sort="Michel, Julien" uniqKey="Michel J" first="Julien" last="Michel">Julien Michel</name>
<name sortKey="Pouget, Marc" sort="Pouget, Marc" uniqKey="Pouget M" first="Marc" last="Pouget">Marc Pouget</name>
</country>
</tree>
</affiliations>
</record>

Pour manipuler ce document sous Unix (Dilib)

EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration

HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000104 | SxmlIndent | more

HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000104 | SxmlIndent | more

Pour mettre un lien sur cette page dans le réseau Wicri

{{Explor lien
   |wiki=    Wicri/Lorraine
   |area=    InforLorV4
   |flux=    Main
   |étape=   Exploration
   |type=    RBID
   |clé=     Hal:hal-01289699
   |texte=   Silhouette of a random polytope
}}

This area was generated with Dilib version V0.6.33.
Data generation: Mon Jun 10 21:56:28 2019. Site generation: Fri Feb 25 15:29:27 2022

	Serveur d'exploration sur la recherche en informatique en Lorraine
	Attention, ce site est en cours de développement ! Attention, site généré par des moyens informatiques à partir de corpus bruts. Les informations ne sont donc pas validées.

Serveur d'exploration sur la recherche en informatique en Lorraine

Silhouette of a random polytope

Silhouette of a random polytope

Source :

Abstract

Links toward previous steps (curation, corpus...)

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri