Remarks on the one-point density of Hele-Shaw $\beta$-ensembles
Year: 2025
Type: article
Abstract: In this note, we prove equicontinuity for the family of one-point densities with respect to a two-dimensional Coulomb gas at an inverse temperature \beta\ge 1/2 confined by an external potential of Hele-Shaw (or quasi-harmonic) type. As a consequence, subsequential limiting Lipschitz continuous densities are defined on the microscopic scale. There are several additional results, for example comparing the one-point density with the thermal equilibrium density.
DOI: 10.4171/rmi/1559
Authors: Yacin Ameur, Erik Troedsson
Institution: Lund University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409814333