Dynamic random walks on Clifford algebras

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

Multiplicative random walks with dynamic transitions are defined on Clifford algebras of arbitrary signature. These multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed.

Mots clés: Clifford algebras; random walks; dynamical systems; hypercubes

Domaines: Probabilités [math.PR]

René Schott, Stacey Staples. Dynamic random walks on Clifford algebras. Advances in Pure and Applied Mathematics, 2010, 1 (1), pp.81-115. ⟨10.1515/apam.2010.007⟩. ⟨hal-00265802⟩