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On Bulk Singularities in the Random Normal Matrix Model

Ameur, Yacin LU and Seo, Seong Mi (2018) In Constructive Approximation 47(1). p.3-37
Abstract

We extend the method of rescaled Ward identities of Ameur, Kang, and Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e., a point in the interior of the droplet where the density of the classical equilibrium measure vanishes. We prove results to the effect that a certain “dominant part” of the Taylor expansion determines the microscopic properties near a bulk2 singularity. A description of the distribution is given in terms of the Bergman kernel of a certain Fock-type space of entire functions.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Bulk singularity, Fock space, Microscopic density, Two-dimensional eigenvalue ensemble, Ward’s equation
in
Constructive Approximation
volume
47
issue
1
pages
3 - 37
publisher
Springer
external identifiers
  • scopus:85012207031
ISSN
0176-4276
DOI
10.1007/s00365-017-9368-4
language
English
LU publication?
yes
id
ea10ad32-fbd6-4ae9-a16f-0d4876c41b5b
date added to LUP
2017-02-22 13:28:26
date last changed
2022-04-01 06:53:22
@article{ea10ad32-fbd6-4ae9-a16f-0d4876c41b5b,
  abstract     = {{<p>We extend the method of rescaled Ward identities of Ameur, Kang, and Makarov to study the distribution of eigenvalues close to a bulk singularity, i.e., a point in the interior of the droplet where the density of the classical equilibrium measure vanishes. We prove results to the effect that a certain “dominant part” of the Taylor expansion determines the microscopic properties near a bulk2 singularity. A description of the distribution is given in terms of the Bergman kernel of a certain Fock-type space of entire functions.</p>}},
  author       = {{Ameur, Yacin and Seo, Seong Mi}},
  issn         = {{0176-4276}},
  keywords     = {{Bulk singularity; Fock space; Microscopic density; Two-dimensional eigenvalue ensemble; Ward’s equation}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{3--37}},
  publisher    = {{Springer}},
  series       = {{Constructive Approximation}},
  title        = {{On Bulk Singularities in the Random Normal Matrix Model}},
  url          = {{http://dx.doi.org/10.1007/s00365-017-9368-4}},
  doi          = {{10.1007/s00365-017-9368-4}},
  volume       = {{47}},
  year         = {{2018}},
}