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Random walks on finite rank solvable groups

Random walks on finite rank solvable groups 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.) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Random walks on finite rank solvable groups

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Publisher
Springer Journals
Copyright
Copyright © 2003 by Springer-Verlag
Subject
Mathematics
ISSN
1435-9855
eISSN
1435-9863
DOI
10.1007/s10097-003-0054-4
Publisher site
See Article on Publisher Site

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.)

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: Sep 5, 2003

References