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Random walks on finite rank solvable groups

Authors
  • Pittet, Ch.1
  • Saloff-Coste, L.2
  • 1 Université Paul Sabatier, Laboratoire de Mathématiques Emile Picard, 118 route de Narbonne, Toulouse, 31062, France , Toulouse
  • 2 Cornell University, Department of Mathematics, 310 Malott Hall, Ithaca, NY, 14853-4201, USA , Ithaca
Type
Published Article
Journal
Journal of the European Mathematical Society
Publisher
Springer-Verlag
Publication Date
Sep 05, 2003
Volume
5
Issue
4
Pages
313–342
Identifiers
DOI: 10.1007/s10097-003-0054-4
Source
Springer Nature
Keywords
License
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Abstract

We establish the lower bound p2t(e,e)≿exp(-t1/3), for the large times asymptotic behaviours of the probabilities p2t(e,e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r, such that any of its finitely generated subgroup admits a generating set of cardinality less or equal to r.)

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