TY - CHAP

T1 - Boundaries of Zn-free groups

AU - Малютин, Андрей Валерьевич

AU - Смирнова-Нагнибеда, Татьяна

AU - Сербин, Денис

N1 - A.Malyutin, T.Smirnova-Nagnibeda, D.Serbin. Boundaries of Zn-free groups // in: Groups, Graphs and Random Walks. London Mathematical Society Lecture Note Series .— 2017.— Vol. 436.— P. 354-388.

PY - 2017

Y1 - 2017

N2 - In this paper, we study random walks on a finitely generated group G which has a free action on a Zn-tree. We show that if G is non-abelian and acts minimally, freely and without inversions on a locally finite Zn-tree Γ with the set of open ends Ends(Γ), then for every non-degenerate probability measure μ on G there exists a unique μ-stationary probability measure νμ on Ends(Γ), and the space (Ends(Γ),νμ) is a μ-boundary. Moreover, if μ has finite first moment with respect to the word metric on G (induced by a finite generating set), then the measure space (Ends(Γ),ν_μ) is isomorphic to the Poisson–Furstenberg boundary of (G, μ).

AB - In this paper, we study random walks on a finitely generated group G which has a free action on a Zn-tree. We show that if G is non-abelian and acts minimally, freely and without inversions on a locally finite Zn-tree Γ with the set of open ends Ends(Γ), then for every non-degenerate probability measure μ on G there exists a unique μ-stationary probability measure νμ on Ends(Γ), and the space (Ends(Γ),νμ) is a μ-boundary. Moreover, if μ has finite first moment with respect to the word metric on G (induced by a finite generating set), then the measure space (Ends(Γ),ν_μ) is isomorphic to the Poisson–Furstenberg boundary of (G, μ).

U2 - 10.1017/9781316576571.015

DO - 10.1017/9781316576571.015

M3 - Article in an anthology

VL - 436

T3 - London Mathematical Society Lecture Note Series

SP - 354

EP - 388

BT - London Mathematical Society Lecture Note Series. Vol. 436.

A2 - Ceccherini-Silberstein, Tullio

A2 - Salvatori, Maura

A2 - Sava-Huss, Ecaterina

PB - Cambridge University Press

ER -