Matrix valued Brownian motion and a paper by Polya

Philippe Biane (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

We give a geometric description of the motion of eigenvalues of a Brownian motion with values in some matrix spaces. In the second part we consider a paper by Polya where he introduced a function close to the Riemann zeta function, which satisfies Riemann hypothesis. We show that each of these two functions can be related to Brownian motion on a symmetric space.

Mots clés: Brownian motion; Symmetric spaces; Riemann zeta function

Domaines: Probabilités [math.PR]; Théorie des nombres [math.NT]; Théorie des représentations [math.RT]

Philippe Biane. Matrix valued Brownian motion and a paper by Polya. Séminaire de Probabilités XLII, 2009, ⟨10.1007/978-3-642-01763-6_7⟩. ⟨hal-00337882⟩