  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.
