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- Title
Poisson-Furstenberg boundary of random walks on wreath products and free metabelian groups.
- Authors
Erschler, Anna
- Abstract
We study the Poisson-Furstenberg boundary of random walks on C = A ≀ B, where A = Zd and B is a finitely generated group having at least 2 elements. We show that for d ≥ 5, for any measure on C such that its third moment is finite and the support of the measure generates C as a group, the Poisson boundary can be identified with the limit "lamplighter" configurations on A. This provides a partial answer to a question of Kaimanovich and Vershik [44]. Also, for free metabelian groups Sd,2 on d generators, d ≥ 5, we answer a question of Vershik [56] and give a complete description of the Poisson-Furstenberg boundary for any non-degenerate random walk on Sd,2 having finite third moment. Finally, we give various examples of slowly decaying measures on wreath products with non-standard boundaries.
- Subjects
FREE metabelian groups; ABELIAN groups; FREE groups; MATHEMATICAL functions; GROUP theory; DIFFERENTIAL equations
- Publication
Commentarii Mathematici Helvetici, 2011, Vol 86, Issue 1, p113
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/220