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Random walks on finite rank solvable groups

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Journal of the European Mathematical Society

Abstract

We establish the lower bound p 2t (e,e)≿exp(-t 1/3), for the large times asymptotic behaviours of the probabilities p 2t (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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Authors and Affiliations

  1. Laboratoire de Mathématiques Emile Picard, Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse, France

    Ch. Pittet

  2. Department of Mathematics, Cornell University, 310 Malott Hall, 14853-4201, Ithaca, NY, USA

    L. Saloff-Coste

Authors
  1. Ch. Pittet
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  2. L. Saloff-Coste
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Correspondence to Ch. Pittet or L. Saloff-Coste.

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Mathematics Subject Classification (2000)

20F16, 20F69, 82B41

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Pittet, C., Saloff-Coste, L. Random walks on finite rank solvable groups. J. Eur. Math. Soc. 5, 313–342 (2003). https://doi.org/10.1007/s10097-003-0054-4

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  • DOI: https://doi.org/10.1007/s10097-003-0054-4

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