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Izvestiya: Mathematics, 2008, Volume 72, Issue 6, Pages 1161–1186
DOI: https://doi.org/10.1070/IM2008v072n06ABEH002432 (Mi im2685) 		 
This article is cited in 4 scientific papers (total in 5 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
English version PDF (534 kB) Citations (5)
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DOI: https://doi.org/10.1070/IM2008v072n06ABEH002432
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.
Received: 21.06.2007
Revised: 17.11.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2008, Volume 72, Issue 6, Pages 105–132
DOI: https://doi.org/10.4213/im2685
Bibliographic databases:
UDC: 514.1, 519.216, 515.162.8, 514.15
MSC: 60J50, 20F36, 37A35, 37A50
Language: English
Original paper language: Russian
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 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:396
    English version PDF:9
    References:92
    First page:19
     
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