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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.

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Dr. Gregory Schehr, University Paris-Sud
Seminarraum Theoretische Physik
Contact: not specified