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Phase transition in the exit boundary problem for random walks on groups. / Vershik, A. M.; Malyutin, A. V.

In: Functional Analysis and its Applications, Vol. 49, No. 2, 19.04.2015, p. 86-96.

Research output: Contribution to journal › Article › peer-review

Harvard

Vershik, AM & Malyutin, AV 2015, 'Phase transition in the exit boundary problem for random walks on groups', Functional Analysis and its Applications, vol. 49, no. 2, pp. 86-96. https://doi.org/10.1007/s10688-015-0090-3

APA

Vershik, A. M., & Malyutin, A. V. (2015). Phase transition in the exit boundary problem for random walks on groups. Functional Analysis and its Applications, 49(2), 86-96. https://doi.org/10.1007/s10688-015-0090-3

Vancouver

Vershik AM, Malyutin AV. Phase transition in the exit boundary problem for random walks on groups. Functional Analysis and its Applications. 2015 Apr 19;49(2):86-96. https://doi.org/10.1007/s10688-015-0090-3

Author

Vershik, A. M. ; Malyutin, A. V. / Phase transition in the exit boundary problem for random walks on groups. In: Functional Analysis and its Applications. 2015 ; Vol. 49, No. 2. pp. 86-96.

BibTeX

@article{1c15ccd711954b19b6f36aad37dd907f,
title = "Phase transition in the exit boundary problem for random walks on groups",
abstract = "We describe the full exit boundary of random walks on homogeneous trees, in particular, on free groups. This model exhibits a phase transition; namely, the family of Markov measures under study loses ergodicity as a parameter of the random walk changes. The problem under consideration is a special case of the problem of describing the invariant (central) measures on branching graphs, which covers a number of problems in combinatorics, representation theory, and probability and was fully stated in a series of recent papers by the first author [1]–[3]. On the other hand, in the context of the theory of Markov processes, close problems were discussed as early as 1960s by E. B. Dynkin.",
keywords = "Bratteli diagram, central measure, de Finetti{\textquoteright}s theorem, dynamic Cayley graph, free group, homogeneous tree, intrinsic metric, Laplace operator, Markov chain, Martin boundary, pascalization, phase transition, Poisson-Furstenberg boundary, tail filtration",
author = "Vershik, {A. M.} and Malyutin, {A. V.}",
year = "2015",
month = apr,
day = "19",
doi = "10.1007/s10688-015-0090-3",
language = "русский",
volume = "49",
pages = "86--96",
journal = "Functional Analysis and its Applications",
issn = "0016-2663",
publisher = "Springer Nature",
number = "2",

}

RIS

TY - JOUR

T1 - Phase transition in the exit boundary problem for random walks on groups

AU - Vershik, A. M.

AU - Malyutin, A. V.

PY - 2015/4/19

Y1 - 2015/4/19

N2 - We describe the full exit boundary of random walks on homogeneous trees, in particular, on free groups. This model exhibits a phase transition; namely, the family of Markov measures under study loses ergodicity as a parameter of the random walk changes. The problem under consideration is a special case of the problem of describing the invariant (central) measures on branching graphs, which covers a number of problems in combinatorics, representation theory, and probability and was fully stated in a series of recent papers by the first author [1]–[3]. On the other hand, in the context of the theory of Markov processes, close problems were discussed as early as 1960s by E. B. Dynkin.

AB - We describe the full exit boundary of random walks on homogeneous trees, in particular, on free groups. This model exhibits a phase transition; namely, the family of Markov measures under study loses ergodicity as a parameter of the random walk changes. The problem under consideration is a special case of the problem of describing the invariant (central) measures on branching graphs, which covers a number of problems in combinatorics, representation theory, and probability and was fully stated in a series of recent papers by the first author [1]–[3]. On the other hand, in the context of the theory of Markov processes, close problems were discussed as early as 1960s by E. B. Dynkin.

KW - Bratteli diagram

KW - central measure

KW - de Finetti’s theorem

KW - dynamic Cayley graph

KW - free group

KW - homogeneous tree

KW - intrinsic metric

KW - Laplace operator

KW - Markov chain

KW - Martin boundary

KW - pascalization

KW - phase transition

KW - Poisson-Furstenberg boundary

KW - tail filtration

UR - http://www.scopus.com/inward/record.url?scp=84935832995&partnerID=8YFLogxK

U2 - 10.1007/s10688-015-0090-3

DO - 10.1007/s10688-015-0090-3

M3 - статья

AN - SCOPUS:84935832995

VL - 49

SP - 86

EP - 96

JO - Functional Analysis and its Applications

JF - Functional Analysis and its Applications

SN - 0016-2663

IS - 2

ER -

ID: 47487792