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Positive definite functions and cut-off for discrete groups

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

Published online by Cambridge University Press:  22 June 2020

Amaury Freslon
Amaury Freslon*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405Orsay, France
*
e-mail: amaury.freslon@math.u-psud.fr
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Abstract

We consider the sequence of powers of a positive definite function on a discrete group. Taking inspiration from random walks on compact quantum groups, we give several examples of situations where a cut-off phenomenon occurs for this sequence, including free groups and infinite Coxeter groups. We also give examples of absence of cut-off using free groups again.

Keywords

Cut-off phenomenonpositive definite functiongeometric group theory

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization

Information

Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 306 - 322
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Copyright
© Canadian Mathematical Society 2020

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