Non-intersecting Brownian walkers and Yang-Mills theory on the sphere

Peter J. Forrester (1) , Satya N. Majumdar (2) , Gregory Schehr (3)

1 Department of Mathematics and Statistics [Melbourne]
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

A scaling regime about the mean of the maximal height of N non-intersecting Brownian excursions ("watermelons" with a wall) is identified, for which the distribution function is identical to that of the scaled largest eigenvalue of GOE random matrices. Large deviation formulas for the maximum height are also computed. Our study relies on a direct correspondence between the distribution function, and the partition function for Yang-Mills theory on a sphere with the gauge group Sp(2N). We also show how known results for the asymptotic analysis of the partition function for Yang-Mills theory on the sphere with gauge group U(N) can be used to study return probabilities for non-intersecting Brownian walkers on a circle.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Peter J. Forrester, Satya N. Majumdar, Gregory Schehr. Non-intersecting Brownian walkers and Yang-Mills theory on the sphere. Nuclear Physics B, 2011, 844 (3), pp.500-526. ⟨10.1016/j.nuclphysb.2010.11.013⟩. ⟨hal-00519636⟩