Random symmetric matrices on Clifford algebras

Dominique Bakry (1, 2) , Marguerite Zani (3)

1 IUF - Institut universitaire de France
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider Brownian motions and other processes (Ornstein-Uhlenbeck processes, spherical Brownian motions) on various sets of symmetric matrices constructed from algebra structures, and look at their associated spectral measure processes. This leads to the identification of the multiplicity of the eigenvalues, together with the identification of the spectral measures. For Clifford algebras, we thus recover Bott's periodicity.

Mots clés: Random matrices; Diffusion operators; Bott's periodicity; Clifford algebras

Domaines: Probabilités [math.PR]

Dominique Bakry, Marguerite Zani. Random symmetric matrices on Clifford algebras. 2013. ⟨hal-00921791⟩