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Boundaries of Zn-free groups. / Малютин, Андрей Валерьевич; Смирнова-Нагнибеда, Татьяна; Сербин, Денис.

London Mathematical Society Lecture Note Series. Vol. 436.: Groups, Graphs and Random Walks. ed. / Tullio Ceccherini-Silberstein; Maura Salvatori; Ecaterina Sava-Huss. Vol. 436 Cambridge University Press, 2017. p. 354-388 (London Mathematical Society Lecture Note Series; Vol. 436).

Research output: Chapter in Book/Report/Conference proceeding › Article in an anthology › peer-review

Harvard

Малютин, АВ, Смирнова-Нагнибеда, Т & Сербин, Д 2017, Boundaries of Zn-free groups. in T Ceccherini-Silberstein, M Salvatori & E Sava-Huss (eds), London Mathematical Society Lecture Note Series. Vol. 436.: Groups, Graphs and Random Walks. vol. 436, London Mathematical Society Lecture Note Series, vol. 436, Cambridge University Press, pp. 354-388. https://doi.org/10.1017/9781316576571.015

APA

Малютин, А. В., Смирнова-Нагнибеда, Т., & Сербин, Д. (2017). Boundaries of Zn-free groups. In T. Ceccherini-Silberstein, M. Salvatori, & E. Sava-Huss (Eds.), London Mathematical Society Lecture Note Series. Vol. 436.: Groups, Graphs and Random Walks (Vol. 436, pp. 354-388). (London Mathematical Society Lecture Note Series; Vol. 436). Cambridge University Press. https://doi.org/10.1017/9781316576571.015

Vancouver

Малютин АВ, Смирнова-Нагнибеда Т, Сербин Д. Boundaries of Zn-free groups. In Ceccherini-Silberstein T, Salvatori M, Sava-Huss E, editors, London Mathematical Society Lecture Note Series. Vol. 436.: Groups, Graphs and Random Walks. Vol. 436. Cambridge University Press. 2017. p. 354-388. (London Mathematical Society Lecture Note Series). https://doi.org/10.1017/9781316576571.015

Author

Малютин, Андрей Валерьевич ; Смирнова-Нагнибеда, Татьяна ; Сербин, Денис. / Boundaries of Zn-free groups. London Mathematical Society Lecture Note Series. Vol. 436.: Groups, Graphs and Random Walks. editor / Tullio Ceccherini-Silberstein ; Maura Salvatori ; Ecaterina Sava-Huss. Vol. 436 Cambridge University Press, 2017. pp. 354-388 (London Mathematical Society Lecture Note Series).

BibTeX

@inbook{8689e44b41a04784a35b4ec60d4a040e,
title = "Boundaries of Zn-free groups",
abstract = "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).",
author = "Малютин, {Андрей Валерьевич} and Татьяна Смирнова-Нагнибеда and Денис Сербин",
note = "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.",
year = "2017",
doi = "10.1017/9781316576571.015",
language = "English",
volume = "436",
series = "London Mathematical Society Lecture Note Series",
publisher = "Cambridge University Press",
pages = "354--388",
editor = "Tullio Ceccherini-Silberstein and Maura Salvatori and Ecaterina Sava-Huss",
booktitle = "London Mathematical Society Lecture Note Series. Vol. 436.",
address = "United Kingdom",

}

RIS

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 -

ID: 15680981