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The Two-Dimensional Coulomb Gas : Fluctuations Through a Spectral Gap

Ameur, Yacin LU ; Charlier, Christophe LU and Cronvall, Joakim LU (2025) In Archive for Rational Mechanics and Analysis 249(6).
Abstract

We study a class of radially symmetric Coulomb gas ensembles at inverse temperature β=2, for which the droplet consists of a number of concentric annuli, having at least one bounded “gap” G, i.e., a connected component of the complement of the droplet, which disconnects the droplet. Let n be the total number of particles. Among other things, we deduce fine asymptotics as n→∞ for the edge density and the correlation kernel near the gap, as well as for the cumulant generating function of fluctuations of smooth linear statistics. We typically find an oscillatory behaviour in the distribution of particles which fall near the edge of the gap. These oscillations are given explicitly in terms of a discrete Gaussian distribution, weighted Szegő... (More)

We study a class of radially symmetric Coulomb gas ensembles at inverse temperature β=2, for which the droplet consists of a number of concentric annuli, having at least one bounded “gap” G, i.e., a connected component of the complement of the droplet, which disconnects the droplet. Let n be the total number of particles. Among other things, we deduce fine asymptotics as n→∞ for the edge density and the correlation kernel near the gap, as well as for the cumulant generating function of fluctuations of smooth linear statistics. We typically find an oscillatory behaviour in the distribution of particles which fall near the edge of the gap. These oscillations are given explicitly in terms of a discrete Gaussian distribution, weighted Szegő kernels, and the Jacobi theta function, which depend on the parameter n.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Archive for Rational Mechanics and Analysis
volume
249
issue
6
article number
63
publisher
Springer
external identifiers
  • scopus:105018027491
ISSN
0003-9527
DOI
10.1007/s00205-025-02133-9
language
English
LU publication?
yes
id
7ff3dd20-3d60-4a1d-8c6a-16dfd648a0b5
date added to LUP
2025-11-20 15:25:35
date last changed
2025-11-20 15:26:35
@article{7ff3dd20-3d60-4a1d-8c6a-16dfd648a0b5,
  abstract     = {{<p>We study a class of radially symmetric Coulomb gas ensembles at inverse temperature β=2, for which the droplet consists of a number of concentric annuli, having at least one bounded “gap” G, i.e., a connected component of the complement of the droplet, which disconnects the droplet. Let n be the total number of particles. Among other things, we deduce fine asymptotics as n→∞ for the edge density and the correlation kernel near the gap, as well as for the cumulant generating function of fluctuations of smooth linear statistics. We typically find an oscillatory behaviour in the distribution of particles which fall near the edge of the gap. These oscillations are given explicitly in terms of a discrete Gaussian distribution, weighted Szegő kernels, and the Jacobi theta function, which depend on the parameter n.</p>}},
  author       = {{Ameur, Yacin and Charlier, Christophe and Cronvall, Joakim}},
  issn         = {{0003-9527}},
  language     = {{eng}},
  number       = {{6}},
  publisher    = {{Springer}},
  series       = {{Archive for Rational Mechanics and Analysis}},
  title        = {{The Two-Dimensional Coulomb Gas : Fluctuations Through a Spectral Gap}},
  url          = {{http://dx.doi.org/10.1007/s00205-025-02133-9}},
  doi          = {{10.1007/s00205-025-02133-9}},
  volume       = {{249}},
  year         = {{2025}},
}