SMS scnews item created by donnelly at Thu 3 Jul 2014 1203
Type: Seminar
Distribution: World
Expiry: 4 Jul 2014
Calendar1: 3 Jul 2014 1500-1600
CalLoc1: Carslaw 451
Auth: donnelly@seurat.maths.usyd.edu.au

# Computational Algebra Seminar: Gebhardt -- Normal forms of random braids


Speaker: Volker Gebhardt (UWS)

"Normal forms of random braids"

In this talk, I will report on joint work with Stephen Tawn.

In the course of an experiment analysing statistical properties of samples of random
braids, we made two rather surprising observations: except for an initial and a final
region whose lengths are uniformly bounded, the distributions of the factors of the
normal form of sufficiently long random braids depend neither on the position in the
normal form nor on the lengths of the random braids.

When multiplying the normal form of a braid on the right, the expected number of factors
in the normal form that are modified, called the expected penetration distance, is
bounded uniformly in the length of the braid.

It turns out that these observations can be explained by analysing two regular languages
associated to normal forms of elements of Garside monoids.  More specifically, there is
a simple condition on the growth rates of these regular languages that characterises
those Garside monoids that exhibit the phenomena mentioned above.  In particular, all
Artin--Tits monoids of spherical type do.


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