Extreme value statistics of 2D Gaussian free field: effect of finite domains. (10th December 2015)

• Record Type: Journal Article
• Authors: Cao, X; Rosso, A; Santachiara, R
• Is Part Of: Journal of physics. Volume 49:Number 2(2016)
• Publication Date: 2015-12-10
• Subjects: extreme value statistics -- Gaussian free field -- freezing transition -- random energy model; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/2/02LT02
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study minima statistics of the 2D Gaussian free field (GFF) 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.