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Exponential decay of correlations in the one-dimensional Coulomb gas ensembles

Turova, Tatyana S. LU (2022) In Journal of Mathematical Physics 63(5).
Abstract

We consider the Gibbs measure on the configurations of N particles on R+ with one fixed particle at one end at 0. The potential includes pair-wise Coulomb interactions between any particle and its 2K neighbors. Only when K = 1, the model is within the rank-one operators, and it was treated previously. Here, for the case K ≥ 2, exponentially fast convergence of density distribution for the spacings between particles is proved when N → ∞. In addition, we establish the exponential decay of correlations between the spacings when the number of particles between them is increasing. We treat in detail the case K = 2; when K > 2, the proof works in a similar manner.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal of Mathematical Physics
volume
63
issue
5
article number
053301
publisher
American Institute of Physics (AIP)
external identifiers
  • scopus:85130301347
ISSN
0022-2488
DOI
10.1063/5.0089803
language
English
LU publication?
yes
id
46a0ff82-ba4d-4cf9-a25c-68ea64a0faee
date added to LUP
2022-07-12 11:13:37
date last changed
2022-07-12 11:13:37
@article{46a0ff82-ba4d-4cf9-a25c-68ea64a0faee,
  abstract     = {{<p>We consider the Gibbs measure on the configurations of N particles on R+ with one fixed particle at one end at 0. The potential includes pair-wise Coulomb interactions between any particle and its 2K neighbors. Only when K = 1, the model is within the rank-one operators, and it was treated previously. Here, for the case K ≥ 2, exponentially fast convergence of density distribution for the spacings between particles is proved when N → ∞. In addition, we establish the exponential decay of correlations between the spacings when the number of particles between them is increasing. We treat in detail the case K = 2; when K &gt; 2, the proof works in a similar manner.</p>}},
  author       = {{Turova, Tatyana S.}},
  issn         = {{0022-2488}},
  language     = {{eng}},
  number       = {{5}},
  publisher    = {{American Institute of Physics (AIP)}},
  series       = {{Journal of Mathematical Physics}},
  title        = {{Exponential decay of correlations in the one-dimensional Coulomb gas ensembles}},
  url          = {{http://dx.doi.org/10.1063/5.0089803}},
  doi          = {{10.1063/5.0089803}},
  volume       = {{63}},
  year         = {{2022}},
}