Random Walks on Clifford Algebras as Directed Hypercubes

René Schott (1, 2) , Stacey Staples (3)

1 IECN - Institut Élie Cartan de Nancy
2 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 Department of Mathematics and Statistics - Southern Illinois University

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.

Domaines: Probabilités [math.PR]

René Schott, Stacey Staples. Random Walks on Clifford Algebras as Directed Hypercubes. Markov Processes And Related Fields, 2008, 14, pp.515-542. ⟨hal-00119996⟩