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A Central Limit Theorem and Exponential Correlation Decay for the Coulomb Chain

Ekström, Henrik LU orcid (2025) In Markov Processes and Related Fields 31(2). p.143-170
Abstract

We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as random variables. It is shown that the correlation between clusters of consecutive variables decay exponentially with the number of variables separating them. This result is then used to prove a central limit theorem.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Central Limit Theorem, Coulomb ensemble
in
Markov Processes and Related Fields
volume
31
issue
2
pages
28 pages
publisher
Polymat
external identifiers
  • scopus:105019794842
ISSN
1024-2953
DOI
10.61102/1024-2953-mprf.2025.31.2.004
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025, Polymat Ltd. All rights reserved.
id
dabfa99e-992d-410d-8d73-a16522df8564
date added to LUP
2026-01-15 12:58:20
date last changed
2026-01-15 12:59:03
@article{dabfa99e-992d-410d-8d73-a16522df8564,
  abstract     = {{<p>We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as random variables. It is shown that the correlation between clusters of consecutive variables decay exponentially with the number of variables separating them. This result is then used to prove a central limit theorem.</p>}},
  author       = {{Ekström, Henrik}},
  issn         = {{1024-2953}},
  keywords     = {{Central Limit Theorem; Coulomb ensemble}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{143--170}},
  publisher    = {{Polymat}},
  series       = {{Markov Processes and Related Fields}},
  title        = {{A Central Limit Theorem and Exponential Correlation Decay for the Coulomb Chain}},
  url          = {{http://dx.doi.org/10.61102/1024-2953-mprf.2025.31.2.004}},
  doi          = {{10.61102/1024-2953-mprf.2025.31.2.004}},
  volume       = {{31}},
  year         = {{2025}},
}