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The planar low temperature Coulomb gas: separation and equidistribution

Ameur, Yacin LU and Romero, José Luis (2023) In Revista Matemática Iberoamericana 39(2). p.611-648
Abstract
We consider planar Coulomb systems consisting of a large number nn of repelling point charges in the low temperature regime, where the inverse temperature β grows at least logarithmically in n as n→∞, i.e., β≳log⁡n.

Under suitable conditions on an external potential, we prove results to the effect that the gas is with high probability uniformly separated and equidistributed with respect to the corresponding equilibrium measure (in the given external field).

Our results generalize earlier results about Fekete configurations, i.e., the case β=∞. There are also several auxiliary results which could be of independent interest. For example, our method of proof of equidistribution (a variant of “Landau’s method”) works for... (More)
We consider planar Coulomb systems consisting of a large number nn of repelling point charges in the low temperature regime, where the inverse temperature β grows at least logarithmically in n as n→∞, i.e., β≳log⁡n.

Under suitable conditions on an external potential, we prove results to the effect that the gas is with high probability uniformly separated and equidistributed with respect to the corresponding equilibrium measure (in the given external field).

Our results generalize earlier results about Fekete configurations, i.e., the case β=∞. There are also several auxiliary results which could be of independent interest. For example, our method of proof of equidistribution (a variant of “Landau’s method”) works for general families of configurations which are uniformly separated and which satisfy certain sampling and interpolation inequalities. (Less)
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author
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type
Contribution to journal
publication status
published
subject
in
Revista Matemática Iberoamericana
volume
39
issue
2
pages
38 pages
publisher
EMS Publishing House
external identifiers
  • scopus:85162757197
ISSN
0213-2230
DOI
10.4171/rmi/1340
language
English
LU publication?
yes
id
a8cf5b90-2d0f-45eb-9106-d58271a4fcca
alternative location
https://doi.org/10.4171/rmi/1340
date added to LUP
2023-06-12 17:45:31
date last changed
2023-09-22 04:00:15
@article{a8cf5b90-2d0f-45eb-9106-d58271a4fcca,
  abstract     = {{We consider planar Coulomb systems consisting of a large number nn of repelling point charges in the low temperature regime, where the inverse temperature β grows at least logarithmically in n as n→∞, i.e., β≳log⁡n.<br/><br/>Under suitable conditions on an external potential, we prove results to the effect that the gas is with high probability uniformly separated and equidistributed with respect to the corresponding equilibrium measure (in the given external field).<br/><br/>Our results generalize earlier results about Fekete configurations, i.e., the case β=∞. There are also several auxiliary results which could be of independent interest. For example, our method of proof of equidistribution (a variant of “Landau’s method”) works for general families of configurations which are uniformly separated and which satisfy certain sampling and interpolation inequalities.}},
  author       = {{Ameur, Yacin and Romero, José Luis}},
  issn         = {{0213-2230}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{611--648}},
  publisher    = {{EMS Publishing House}},
  series       = {{Revista Matemática Iberoamericana}},
  title        = {{The planar low temperature Coulomb gas: separation and equidistribution}},
  url          = {{http://dx.doi.org/10.4171/rmi/1340}},
  doi          = {{10.4171/rmi/1340}},
  volume       = {{39}},
  year         = {{2023}},
}