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On boundary confinements for the Coulomb gas

Ameur, Yacin LU ; Kang, Nam Gyu and Seo, Seong Mi LU (2020) In Analysis and Mathematical Physics 10(4).
Abstract

We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well... (More)

We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Hard edge, Planar orthogonal polynomials, Random normal matrices, Scaling limits, Soft edge, Universality
in
Analysis and Mathematical Physics
volume
10
issue
4
article number
68
publisher
Springer
external identifiers
  • scopus:85094673670
ISSN
1664-2368
DOI
10.1007/s13324-020-00406-y
language
English
LU publication?
yes
id
f2970752-d170-416a-8635-08006896702d
date added to LUP
2020-11-13 08:35:12
date last changed
2022-04-26 21:49:18
@article{f2970752-d170-416a-8635-08006896702d,
  abstract     = {{<p>We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined.</p>}},
  author       = {{Ameur, Yacin and Kang, Nam Gyu and Seo, Seong Mi}},
  issn         = {{1664-2368}},
  keywords     = {{Hard edge; Planar orthogonal polynomials; Random normal matrices; Scaling limits; Soft edge; Universality}},
  language     = {{eng}},
  number       = {{4}},
  publisher    = {{Springer}},
  series       = {{Analysis and Mathematical Physics}},
  title        = {{On boundary confinements for the Coulomb gas}},
  url          = {{http://dx.doi.org/10.1007/s13324-020-00406-y}},
  doi          = {{10.1007/s13324-020-00406-y}},
  volume       = {{10}},
  year         = {{2020}},
}