Random walks on braid groups: Brownian bridges, complexity and statistics

S. K. Nechaev, A. Yu Grosberg, A. M. Vershik

    Research output: Contribution to journalArticle

    Abstract

    We investigate the limit behaviour of random walks on some non-commutative discrete groups related to knot theory. Namely, we study the connection between the limit behaviour of the Lyapunov exponent of products of non-commutative random matrices - generators of the braid group - and the asymptotics of powers of the algebraic invariants of randomly generated knots. We turn the simplest problems of knot statistics into the context of random walks on hyperbolic groups. We also consider the limit distribution of Brownian bridges on so-called locally non-commutative groups.

    Original languageEnglish (US)
    Pages (from-to)2411-2433
    Number of pages23
    JournalJournal of Physics A: Mathematical and General
    Volume29
    Issue number10
    DOIs
    StatePublished - 1996

    Fingerprint

    Brownian Bridge
    Braid Group
    random walk
    Random walk
    Limit Behavior
    Statistics
    statistics
    Knot
    Knot Theory
    Hyperbolic Groups
    Discrete Group
    Limit Distribution
    Random Matrices
    Lyapunov Exponent
    Generator
    Invariant
    generators
    exponents
    products

    ASJC Scopus subject areas

    • Physics and Astronomy(all)
    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this

    Random walks on braid groups : Brownian bridges, complexity and statistics. / Nechaev, S. K.; Grosberg, A. Yu; Vershik, A. M.

    In: Journal of Physics A: Mathematical and General, Vol. 29, No. 10, 1996, p. 2411-2433.

    Research output: Contribution to journalArticle

    Nechaev, S. K. ; Grosberg, A. Yu ; Vershik, A. M. / Random walks on braid groups : Brownian bridges, complexity and statistics. In: Journal of Physics A: Mathematical and General. 1996 ; Vol. 29, No. 10. pp. 2411-2433.
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