Graphs, local zeta functions, Log-Coulomb Gases, and phase transitions at finite temperature

W. A. Zúñiga-Galindo, B. A. Zambrano-Luna, Edwin León-Cardenal

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e. R, C, Q_{p} the field of p-adic numbers). In this gas, a log-Coulomb in…