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arXiv · 1310.4265

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

Sebastien Gouezel
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Abstract

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 from 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.

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Sebastien Gouezel. 2014-06-06. A numerical lower bound for the spectral radius of random walks on surface groups. https://doi.org/10.1017/s0963548314000819

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