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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 6, Pages 105–132 (Mi izv2685)  

This article is cited in 2 scientific papers (total in 3 papers)

Boundaries of braid groups and the Markov–Ivanovsky normal form

A. M. Vershik, A. V. Malyutin

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We describe random walk boundaries (in particular, the Poisson–Furstenberg, or PF-, boundary) for a large family of groups in terms of the hyperbolic boundary of a special normal free subgroup. We prove that almost all the trajectories of a random walk (with respect to an arbitrary non-degenerate measure on the group) converge to points of that boundary. This yields the stability (in the sense of [6]) of the so-called Markov–Ivanovsky normal form [12] for braids.

DOI: https://doi.org/10.4213/im2685

Full text: PDF file (1027 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:6, 1161–1186

Bibliographic databases:

UDC: 514.1, 519.216, 515.162.8, 514.15
MSC: 60J50, 20F36, 37A35, 37A50
Received: 21.06.2007
Revised: 17.11.2007

Citation: A. M. Vershik, A. V. Malyutin, “Boundaries of braid groups and the Markov–Ivanovsky normal form”, Izv. RAN. Ser. Mat., 72:6 (2008), 105–132; Izv. Math., 72:6 (2008), 1161–1186

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Erschler A., “Poisson-Furstenberg boundary of random walks on wreath products and free metabelian groups”, Comment. Math. Helv., 86:1 (2011), 113–143  crossref  mathscinet  zmath  isi  elib  scopus
    2. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Malyutin A., Nagnibeda T., Serbin D., “Boundaries of Z(N)-Free Groups”, Groups, Graphs and Random Walks, London Mathematical Society Lecture Note Series, 436, eds. CeccheriniSilberstein T., Salvatori M., SavaHuss E., Cambridge Univ Press, 2017, 355–390  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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