2019/08/01 by Sergii M. Torba, Torba, Sergii M., W. A. Zúñiga‐Galindo +1 · 1 citation
Computer Science · Mathematics · #11Q25 #46S10 #60B10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Primary 82D05 #Probability (math.PR) #Secondary 82B21 #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1908.00571
openalex publication_date 2019/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article aims to study the Coulomb gas model over the d-dimensional p-adic space. We establish the existence of equilibria measures and the Γ-limit for the Coulomb energy functional when the number of configurations tends to infinity. For a cloud of charged particles confined into the unit ball, we compute the equilibrium measure and the minimum of its Coulomb energy functional. In the p-adic setting the Coulomb energy is the continuum limit of the minus a hierarchical Hamiltonian attached to a spin glass model with a p-adic coupling.