Geodesic
Random walks on nilpotent groups driven by measures supported on powers of generators
Laurent Saloff-Coste1 ; Tianyi Zheng2 orcid
1Cornell University, Ithaca, United States
2Stanford University, USA
Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1047-1129

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DOI

We study the decay of convolution powers of a large family μS,a​ of measures on finitely generated nilpotent groups. Here, S=(s1​,...,sk​) is a generating k-tuple of group elements and a=(α1​,...,αk​) is a k-tuple of reals in the interval (0,2). The symmetric measure μS,a​ is supported by S∗={sim​,1≤i≤k,m∈Z} and gives probability proportional to (1+m)−αi​−1 to si±m​, i=1,...,k, m∈N. We determine the behavior of the probability of return μS,a(n)​(e) as n tends to infinity. This behavior depends in somewhat subtle ways on interactions between the k-tuple a and the positions of the generators si​ within the lower central series Gj​=[Gj−1​,G], G1​=G.
DOI : 10.4171/ggd/335
Classification : 20-XX, 60-XX
Mots-clés : Random walk, stable laws, nilpotent groups

Laurent Saloff-Coste  1   ; Tianyi Zheng  2

1 Cornell University, Ithaca, United States
2 Stanford University, USA 
Laurent Saloff-Coste; Tianyi Zheng. Random walks on nilpotent groups driven by measures supported on powers of generators. Groups, geometry, and dynamics, Tome 9 (2015) no. 4, pp. 1047-1129. doi: 10.4171/ggd/335
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     author = {Laurent Saloff-Coste and Tianyi Zheng},
     title = {Random walks on nilpotent groups driven by measures supported on powers of generators},
     journal = {Groups, geometry, and dynamics},
     pages = {1047--1129},
     year = {2015},
     volume = {9},
     number = {4},
     doi = {10.4171/ggd/335},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/335/}
}
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