Boundaries of Zn-free groups

Андрей Валерьевич Малютин, Татьяна Смирнова-Нагнибеда, Денис Сербин

Research output

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).
Original languageEnglish
Title of host publicationLondon Mathematical Society Lecture Note Series. Vol. 436.
Subtitle of host publicationGroups, Graphs and Random Walks
EditorsTullio Ceccherini-Silberstein, Maura Salvatori, Ecaterina Sava-Huss
PublisherCambridge University Press
Pages354-388
Number of pages35
Volume436
ISBN (Electronic)9781316576571
DOIs
Publication statusPublished - 2017

Publication series

NameLondon Mathematical Society Lecture Note Series
PublisherCambridge University Press
Volume436

Cite this

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
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).
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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.",
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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

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

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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