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Remarks on the one-point density of Hele-Shaw β-ensembles

Ameur, Yacin LU and Troedsson, Erik LU (2025) In Revista Matematica Iberoamericana 41(4). p.1555-1582
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 β ≥ 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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
equicontinuity, Hele-Shaw potential, one-point density, thermal equilibrium measure, Ward's identity, β-ensemble
in
Revista Matematica Iberoamericana
volume
41
issue
4
pages
28 pages
publisher
EMS Publishing House
external identifiers
  • scopus:105007633241
ISSN
0213-2230
DOI
10.4171/RMI/1559
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 Real Sociedad Matemática Española.
id
402a2fcb-1c4b-4697-b082-889b26013dc6
date added to LUP
2025-12-16 11:40:51
date last changed
2025-12-19 09:00:36
@article{402a2fcb-1c4b-4697-b082-889b26013dc6,
  abstract     = {{<p>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 β ≥ 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.</p>}},
  author       = {{Ameur, Yacin and Troedsson, Erik}},
  issn         = {{0213-2230}},
  keywords     = {{equicontinuity; Hele-Shaw potential; one-point density; thermal equilibrium measure; Ward's identity; β-ensemble}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1555--1582}},
  publisher    = {{EMS Publishing House}},
  series       = {{Revista Matematica Iberoamericana}},
  title        = {{Remarks on the one-point density of Hele-Shaw β-ensembles}},
  url          = {{http://dx.doi.org/10.4171/RMI/1559}},
  doi          = {{10.4171/RMI/1559}},
  volume       = {{41}},
  year         = {{2025}},
}