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Phase transitions in the one-dimensional coulomb gas ensembles

Turova, Tatyana S. LU (2018) In Annals of Applied Probability 28(2). p.1249-1291
Abstract

We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles... (More)

We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles in the limit when the number of particles goes to infinity. We identify 5 different phases for any positive temperature. The proofs rely on a conditional central limit theorem for nonidentical random variables, which has an interest on its own.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Coulomb gas, Gibbs ensemble., Phase transitions
in
Annals of Applied Probability
volume
28
issue
2
pages
43 pages
publisher
Institute of Mathematical Statistics
external identifiers
  • scopus:85046253733
ISSN
1050-5164
DOI
10.1214/17-AAP1329
language
English
LU publication?
yes
id
c33abb97-df0f-4639-8bd6-cedd5a4e4bda
date added to LUP
2018-05-17 15:20:27
date last changed
2018-05-29 09:45:47
@article{c33abb97-df0f-4639-8bd6-cedd5a4e4bda,
  abstract     = {<p>We consider the system of particles on a finite interval with pairwise nearest neighbours interaction and external force. This model was introduced by Malyshev [Probl. Inf. Transm. 51 (2015) 31–36] to study the flow of charged particles on a rigorous mathematical level. It is a simplified version of a 3-dimensional classical Coulomb gas model. We study Gibbs distribution at finite positive temperature extending recent results on the zero temperature case (ground states). We derive the asymptotics for the mean and for the variances of the distances between the neighbouring charges. We prove that depending on the strength of the external force there are several phase transitions in the local structure of the configuration of the particles in the limit when the number of particles goes to infinity. We identify 5 different phases for any positive temperature. The proofs rely on a conditional central limit theorem for nonidentical random variables, which has an interest on its own.</p>},
  author       = {Turova, Tatyana S.},
  issn         = {1050-5164},
  keyword      = {Coulomb gas,Gibbs ensemble.,Phase transitions},
  language     = {eng},
  month        = {04},
  number       = {2},
  pages        = {1249--1291},
  publisher    = {Institute of Mathematical Statistics},
  series       = {Annals of Applied Probability},
  title        = {Phase transitions in the one-dimensional coulomb gas ensembles},
  url          = {http://dx.doi.org/10.1214/17-AAP1329},
  volume       = {28},
  year         = {2018},
}