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Funktsional. Anal. i Prilozhen., 2013, Volume 47, Issue 2, Pages 84–89 (Mi faa3110)  

This article is cited in 3 scientific papers (total in 3 papers)

Brief communications

Continuity of Asymptotic Characteristics for Random Walks on Hyperbolic Groups

V. A. Kaimanovicha, A. G. Erschlerb

a University of Ottawa
b Paris-Sud University 11

Abstract: We describe a new approach to proving the continuity of asymptotic entropy as a function of a transition measure under a finite first moment condition. It is based on using conditional random walks and amounts to checking uniformity in the strip criterion for the identification of the Poisson boundary. It is applicable to word hyperbolic groups and in several other situations when the Poisson boundary can be identified with an appropriate geometric boundary.

Keywords: random walk, asymptotic entropy, hyperbolic groups

DOI: https://doi.org/10.4213/faa3110

Full text: PDF file (173 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2013, 47:2, 152–156

Bibliographic databases:

UDC: 519.217
Received: 02.07.2012

Citation: V. A. Kaimanovich, A. G. Erschler, “Continuity of Asymptotic Characteristics for Random Walks on Hyperbolic Groups”, Funktsional. Anal. i Prilozhen., 47:2 (2013), 84–89; Funct. Anal. Appl., 47:2 (2013), 152–156

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/faa3110
  • https://doi.org/10.4213/faa3110
  • http://mi.mathnet.ru/eng/faa/v47/i2/p84

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. Mathieu, “Differentiating the entropy of random walks on hyperbolic groups”, Ann. Probab., 43:1 (2015), 166–187  crossref  mathscinet  zmath  isi  scopus
    2. S. Gouezel, F. Matheus, F. Maucourant, “Entropy and drift in word hyperbolic groups”, Invent. Math., 211:3 (2018), 1201–1255  crossref  mathscinet  zmath  isi  scopus
    3. Tanaka R., “Dimension of Harmonic Measures in Hyperbolic Spaces”, Ergod. Theory Dyn. Syst., 39:2 (2019), 474–499  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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