Extreme value statistics of 2d Gaussian Free Field: effect of finite domains

Xiangyu Cao 1 Alberto Rosso 1 Raoul Santachiara 1

Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2016, 49, pp.02LT02

We study minima statistics of the 2d Gaussian Free Field on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated Random Energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques