2015/09/30 by Xiangyu Cao, X Cao, Alberto Rosso +3
Mathematics · Physics and Astronomy · #Boundary (topology) #Boundary value problem #Dirichlet distribution #Energy (signal processing) #Extreme value theory #Field (mathematics) #Gaussian #Gaussian free field #Geometry and complex manifolds #Maxima and minima #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/49/2/02lt02
published as J. Phys. A: Math. Theor. 49 02LT02 (2016) · 8 pages, 4 figures. Modified version accepted by J. Phys. A: Math. Theo
arxiv created 2015/11/24 · openalex publication_date 2015/12/10 · arxiv updated 2015/12/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.