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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Random walks on abelian-by-cyclic groups


Authors: Christophe Pittet and Laurent Saloff-Coste
Journal: Proc. Amer. Math. Soc. 131 (2003), 1071-1079
MSC (2000): Primary 20F69, 82B41, 60B99, 20F16
Published electronically: September 5, 2002
MathSciNet review: 1948097
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Abstract: We describe the large time asymptotic behaviors of the probabilities $p_{2t}(e,e)$ of return to the origin associated to finite symmetric generating sets of abelian-by-cyclic groups. We characterize the different asymptotic behaviors by simple algebraic properties of the groups.


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Additional Information

Christophe Pittet
Affiliation: Laboratoire Emile Picard, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France
Email: pittet@picard.ups-tlse.fr

Laurent Saloff-Coste
Affiliation: Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, New York 14853-4201
Email: lsc@math.cornell.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06674-1
PII: S 0002-9939(02)06674-1
Keywords: Random walk, heat kernel decay, asymptotic invariants of infinite groups, metabelian groups
Received by editor(s): August 6, 2001
Received by editor(s) in revised form: November 19, 2001
Published electronically: September 5, 2002
Additional Notes: The first author was supported by a Delegation CNRS at UMR 5580
The second author was supported by NSF grant DMS-9802855
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2002 American Mathematical Society