We consider Brownian motions and other processes (Ornstein-Uhlenbeck processes, spherical Brownian motions) on various sets of symmetric matrices constructed from algebra, 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.
CITATION STYLE
Bakry, D., & Zani, M. (2014). Dyson processes associated with associative algebras: The clifford case. Lecture Notes in Mathematics, 2116. https://doi.org/10.1007/978-3-319-09477-9_1
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