A.Vershik.
Random braids, random tangles, Poisson boundary, problems.
Abstract.
Random braids or random tangles can be defined in the various ways.
The simplest one is just uses theory of random walks on the groups and
on the homogeneous spaces. The first problem - to describe asymptotic
behaviour of the most likely in the senseof probability braid (or
knot, so on). In the recent paper with A.Malyutin the boundary of the
braid gorup
was described using so called Markov-Ivanvsky normal form and
Furstenberg approach, but many problems still are open. We will
discussed them.