Geodesic
Spectral properties of a class of random walks on locally finite groups
Alexander Bendikov1 ; Barbara Bobikau1 ; Christophe Pittet2
1Uniwersytet Wrocławski, Poland
2Aix-Marseille Université, France
Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 791-820

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DOI

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. We obtain examples of fast/slow decays of return probabilities, a recurrence criterion, exact values and estimates of isospectral profiles and spectral distributions.
DOI : 10.4171/ggd/206
Classification : 60-XX, 43-XX, 62-XX
Mots-clés : Random walk, locally finite group, ultra-metric space, infinite divisible distribution, Laplace transform, Köhlbecker transform, Legendre transform, return probability, spectral distribution, isospectral profile

Alexander Bendikov  1   ; Barbara Bobikau  1   ; Christophe Pittet  2

1 Uniwersytet Wrocławski, Poland
2 Aix-Marseille Université, France 
Alexander Bendikov; Barbara Bobikau; Christophe Pittet. Spectral properties of a class of random walks on locally finite groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 4, pp. 791-820. doi: 10.4171/ggd/206
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     doi = {10.4171/ggd/206},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/206/}
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