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Dyubina, Anna

doi:10.1023/a:1012465406149

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A Sufficient Condition For Triviality Of the Poisson-fursten...1

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Cited by 5 publications

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“…Another approach to criteria for triviality of the boundary in the case of ordinary wreath products A ≀ G, in which the induced random walk on G is recurrent, is to estimate the entropy of the random walk [13]. The proposition below is an analogue of such a criterion, but now in the case of permutational wreath products.…”

Section: A Sufficient Condition For Triviality Of the Poisson-fursten...mentioning

confidence: 99%

Poisson–Furstenberg boundary and growth of groups

Bartholdi

Erschler

2016

Probab. Theory Relat. Fields

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Abstract. We study the Poisson-Furstenberg boundary of random walks on permutational wreath products. We give a sufficient condition for a group to admit a symmetric measure of finite first moment with non-trivial boundary, and show that this criterion is useful to establish exponential word growth of groups. We construct groups of exponential growth such that all finitely supported (not necessarily symmetric, possibly degenerate) random walks on these groups have trivial boundary. This gives a negative answer to a question of Kaimanovich and Vershik.

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Section: A Sufficient Condition For Triviality Of the Poisson-fursten...mentioning

confidence: 99%

Poisson–Furstenberg boundary and growth of groups

Bartholdi

Erschler

2016

Probab. Theory Relat. Fields

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On Continuity of Range, Entropy and Drift for Random Walks on Groups

Erschler

2011

Random Walks, Boundaries and Spectra

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Rate of escape on the lamplighter tree

Gilch

2008

J Math Sci

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Abstract. Suppose we are given a homogeneous tree Tq of degree q ≥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product (Z/2) ≀ Γ, where Γ = * q i=1 Z/2 is the free product group of q factors Z/2. We consider a transient random walk on a Cayley graph of (Z/2) ≀ Γ, for which we want to compute lower and upper bounds for the rate of escape, that is, the speed at which the random walk flees to infinity.

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Cited by 5 publications

References 2 publications

Poisson–Furstenberg boundary and growth of groups

Poisson–Furstenberg boundary and growth of groups

On Continuity of Range, Entropy and Drift for Random Walks on Groups

Rate of escape on the lamplighter tree

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