On the stability of the behavior of random walks on groups

Pittet, Ch.; Saloff‐Coste, Laurent

doi:10.1007/bf02921994

Cited by 68 publications

(55 citation statements)

References 20 publications

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“…This rate is a geometric invariant of the group G. See for instance [5], [41], [43]. In particular, let G be an abelian non-compact compactly generated group.…”

Section: Proposition 42 a Random Walk On G With Law µ = µ(C) Is Recmentioning

confidence: 99%

Spectral properties of a class of random walks on locally finite groups

Bendikov¹,

Bobikau²,

Pittet³

2013

Groups Geom. Dyn.

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Abstract. We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group S ∞ . On locally finite groups, the random walks under consideration are driven by infinite divisible distributions. This allows us to embed our random walks into continuous time Lévy processes whose heat kernels have shapes similar to the ones of α-stable processes. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions, formulae and estimates for the escape rates and for heat kernels.

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“…This rate is a geometric invariant of the group G. See for instance [5], [41], [43]. In particular, let G be an abelian non-compact compactly generated group.…”

Section: Proposition 42 a Random Walk On G With Law µ = µ(C) Is Recmentioning

confidence: 99%

Spectral properties of a class of random walks on locally finite groups

Bendikov¹,

Bobikau²,

Pittet³

2013

Groups Geom. Dyn.

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“…Furthermore, Pittet and Saloff-Coste [25] showed that the decay order of the probability of return after 2n-steps to the starting point does not change under the quasi-isometry. Since a nilpotent covering graph X and its covering transformation group Γ are quasi-isometric, the Gaussian upper bound for k n on X (Theorem 4, (1.7)) is deduced from their results (see also Saloff-Coste [29]).…”

Section: If X Is a Bipartite Graph With A Bipartition V = A B Andmentioning

confidence: 99%

“…Then we have Theorem 4 (Gaussian estimates cf. [25], [15]). There exist constants C and C > 0 such that the following hold:…”

Section: If X Is a Bipartite Graph With A Bipartition V = A B Andmentioning

confidence: 99%

Geometric and analytic properties in the behavior of random walks on nilpotent covering graphs

Ishiwata¹

2004

Tohoku Math. Publ.

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“…In [8], Pittet and Saloff-Coste studied the relationship between the return probability of a symmetric random walk on a finitely generated group and the heat kernel on a co-compact covering manifold of the group. Let p n (e, e) represent the n-step return probability of the random walk on the group.…”

Section: Introductionmentioning

confidence: 99%