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Article Dans Une Revue Combinatorics, Probability and Computing Année : 2015

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

Résumé

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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Dates et versions

hal-00873167 , version 1 (15-10-2013)
hal-00873167 , version 2 (06-06-2014)

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Citer

Sebastien Gouezel. A numerical lower bound for the spectral radius of random walks on surface groups. Combinatorics, Probability and Computing, 2015, 24 (6), pp.838-856. ⟨10.1017/S0963548314000819⟩. ⟨hal-00873167v2⟩
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