A numerical lower bound for the spectral radius of random walks on surface groups

Sebastien Gouezel (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

Estimating numerically the spectral radius of a random walk on a nonamenable graph is complicated, since the cardinality of balls grows exponentially fast with the radius. We propose an algorithm to get a bound for below for this spectral radius in Cayley graphs with finitely many cone types (including for instance hyperbolic groups). In the genus $2$ surface group, it improves by an order of magnitude the previous best bound, due to Bartholdi.

Mots clés: spectral radius; cogrowth; numerical algorithm; surface groups

Domaines: Probabilités [math.PR]

Sebastien Gouezel. A numerical lower bound for the spectral radius of random walks on surface groups. 2013. ⟨hal-00873167v1⟩