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The Random Normal Matrix Model : Insertion of a Point Charge

Ameur, Yacin LU ; Kang, Nam-Gyu and Seo, Seong-Mi (2021) In Potential Analysis 2021.
Abstract
In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits (“Mittag-Leffler fields”) and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log|pn(ζ)| where pn is the characteristic polynomial of an n:th order random normal matrix.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Planar Coulomb gas, Microscopic limit, Conical limit, Fock-Sobolev space, Ward's equation
in
Potential Analysis
volume
2021
pages
42 pages
publisher
Springer
external identifiers
  • scopus:85111796183
ISSN
1572-929X
DOI
10.1007/s11118-021-09942-z
language
English
LU publication?
yes
id
28f04de6-7967-4682-aaa8-1d6f814dd2ec
date added to LUP
2021-12-15 17:04:02
date last changed
2025-10-14 08:55:01
@article{28f04de6-7967-4682-aaa8-1d6f814dd2ec,
  abstract     = {{In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits (“Mittag-Leffler fields”) and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log|pn(ζ)| where pn is the characteristic polynomial of an n:th order random normal matrix.}},
  author       = {{Ameur, Yacin and Kang, Nam-Gyu and Seo, Seong-Mi}},
  issn         = {{1572-929X}},
  keywords     = {{Planar Coulomb gas; Microscopic limit; Conical limit; Fock-Sobolev space; Ward's equation}},
  language     = {{eng}},
  month        = {{08}},
  publisher    = {{Springer}},
  series       = {{Potential Analysis}},
  title        = {{The Random Normal Matrix Model : Insertion of a Point Charge}},
  url          = {{http://dx.doi.org/10.1007/s11118-021-09942-z}},
  doi          = {{10.1007/s11118-021-09942-z}},
  volume       = {{2021}},
  year         = {{2021}},
}