Random Walks on Clifford Algebras as Directed Hypercubes
Identifieur interne : 004531 ( Main/Exploration ); précédent : 004530; suivant : 004532Random Walks on Clifford Algebras as Directed Hypercubes
Auteurs : René Schott [France] ; Stacey Staples [États-Unis]Source :
Abstract
Given a Clifford algebra of arbitrary signature $Cl_{p+q}=n$ multiplicative random walks are induced by sequences of independent, uniformly distributed random variables taking values in the unit basis paravectors in the algebra. These walks take values in the positive and negative basis multivectors of the algebra and can be treated as random walks on directed hypercubes. Methods of walks on hypercubes are employed to develop limit theorems. These multiplicative walks are then used to induce additive walks on the Clifford algebra. Again, limit theorems are developed.
Url:
Affiliations:
- France, États-Unis
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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<front><div type="abstract" xml:lang="en">Given a Clifford algebra of arbitrary signature $Cl_{p+q}=n$ multiplicative random walks are induced by sequences of independent, uniformly distributed random variables taking values in the unit basis paravectors in the algebra. These walks take values in the positive and negative basis multivectors of the algebra and can be treated as random walks on directed hypercubes. Methods of walks on hypercubes are employed to develop limit theorems. These multiplicative walks are then used to induce additive walks on the Clifford algebra. Again, limit theorems are developed.</div>
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