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

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

    Research output: Contribution to journalArticlepeer-review

    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

    ASJC Scopus subject areas

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

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