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A Numerical Lower Bound for the Spectral Radius of Random Walks on Surface Groups

Part of: Probability theory on algebraic and topological structures Special aspects of infinite or finite groups Graph theory

Published online by Cambridge University Press:  29 January 2015

S. GOUEZEL
S. GOUEZEL*
Affiliation:
IRMAR, CNRS UMR 6625, Université de Rennes 1, 35042 Rennes, France (e-mail: sebastien.gouezel@univ-rennes1.fr)
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Abstract

Estimating numerically the spectral radius of a random walk on a non-amenable 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.

MSC classification

Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups 05C81: Random walks on graphs
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Issue 6 , November 2015 , pp. 838 - 856
Copyright
Copyright © Cambridge University Press 2015 

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