RANDOM-WALKS ON BRAID-GROUPS - BROWNIAN BRIDGES, COMPLEXITY AND STATISTICS

We investigate the limit behaviour of random walks on some non-commuta tive discrete groups related to knot theory. Namely, we study the conn ection between the limit behaviour of the Lyapunov exponent of product s of non-commutative random matrices-generators of the braid group-and the asymptotics of powers of the algebraic invariants of randomly gen erated knots. We turn the simplest problems of knot statistics into th e context of random walks on hyperbolic groups. We also consider the l imit distribution of Brownian bridges on so-called locally non-commuta tive groups.