### 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 language | English (US) |
---|---|

Pages (from-to) | 2411-2433 |

Number of pages | 23 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 29 |

Issue number | 10 |

DOIs | |

State | Published - 1996 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

*29*(10), 2411-2433. https://doi.org/10.1088/0305-4470/29/10/020

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

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 29, no. 10, pp. 2411-2433. https://doi.org/10.1088/0305-4470/29/10/020

}

TY - JOUR

T1 - Random walks on braid groups

T2 - Brownian bridges, complexity and statistics

AU - Nechaev, S. K.

AU - Grosberg, A. Yu

AU - Vershik, A. M.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0008883043&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0008883043&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/29/10/020

DO - 10.1088/0305-4470/29/10/020

M3 - Article

AN - SCOPUS:0008883043

VL - 29

SP - 2411

EP - 2433

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

ER -