Speaker
Gregory Schehr
(Universite Paris-sud)
Description
Non-intersecting random walkers (or "vicious walkers") have
been studied in various physical situations, ranging from
polymer physics to wetting and melting transitions and more
recently in connection with random matrix theory or stochastic
growth processes. In this talk, I will present a method based
on path integrals associated to free Fermions models to study
such statistical systems. I will use this method to calculate
exactly the cumulative distribution function (CDF) of the
maximal height of p vicious walkers with a wall (excursions)
and without a wall (bridges). In the case of excursions, I will
show that the CDF is identical to the partition function of 2d
Yang Mills theory on a sphere with the gauge group Sp(2p).
Taking advantage of a large p analysis achieved in that context,
I will show that the CDF, properly shifted and scaled, converges
to the Tracy-Widom distribution for beta = 1, which describes
the fluctuations of the largest eigenvalue of Random Matrices
in the Gaussian Orthogonal Ensemble.