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A localization theorem for the planar coulomb gas in an external field

Ameur, Yacin LU (2021) In Electronic Journal of Probability 26.
Abstract

We examine a two-dimensional Coulomb gas consisting of n identical repelling point charges at an arbitrary inverse temperature β, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the droplet – the support of the equilibrium measure determined by the external field. More precisely, we prove that the distance between the droplet and the vacuum is with very high probability at most proportional to [Formula Presented]. This order of magnitude is known to be “tight” when β = 1 and the external field is radially symmetric. In addition, we prove estimates for the one-point function in a neighbourhood of the droplet, proving in particular a fast uniform decay as one moves beyond... (More)

We examine a two-dimensional Coulomb gas consisting of n identical repelling point charges at an arbitrary inverse temperature β, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the droplet – the support of the equilibrium measure determined by the external field. More precisely, we prove that the distance between the droplet and the vacuum is with very high probability at most proportional to [Formula Presented]. This order of magnitude is known to be “tight” when β = 1 and the external field is radially symmetric. In addition, we prove estimates for the one-point function in a neighbourhood of the droplet, proving in particular a fast uniform decay as one moves beyond a distance roughly of the order [Formula Presented] from the droplet.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Coulomb gas, Droplet, External potential, Localization
in
Electronic Journal of Probability
volume
26
article number
46
publisher
UNIV WASHINGTON, DEPT MATHEMATICS
external identifiers
  • scopus:85105197893
ISSN
1083-6489
DOI
10.1214/21-EJP613
language
English
LU publication?
yes
id
7070d11e-42d0-4044-b948-66232a26485f
date added to LUP
2021-05-31 14:03:11
date last changed
2025-04-04 14:49:42
@article{7070d11e-42d0-4044-b948-66232a26485f,
  abstract     = {{<p>We examine a two-dimensional Coulomb gas consisting of n identical repelling point charges at an arbitrary inverse temperature β, subjected to a suitable external field. We prove that the gas is effectively localized to a small neighbourhood of the droplet – the support of the equilibrium measure determined by the external field. More precisely, we prove that the distance between the droplet and the vacuum is with very high probability at most proportional to [Formula Presented]. This order of magnitude is known to be “tight” when β = 1 and the external field is radially symmetric. In addition, we prove estimates for the one-point function in a neighbourhood of the droplet, proving in particular a fast uniform decay as one moves beyond a distance roughly of the order [Formula Presented] from the droplet.</p>}},
  author       = {{Ameur, Yacin}},
  issn         = {{1083-6489}},
  keywords     = {{Coulomb gas; Droplet; External potential; Localization}},
  language     = {{eng}},
  publisher    = {{UNIV WASHINGTON, DEPT MATHEMATICS}},
  series       = {{Electronic Journal of Probability}},
  title        = {{A localization theorem for the planar coulomb gas in an external field}},
  url          = {{http://dx.doi.org/10.1214/21-EJP613}},
  doi          = {{10.1214/21-EJP613}},
  volume       = {{26}},
  year         = {{2021}},
}