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On Bulk Singularities in the Random Normal Matrix Model

Ameur, Yacin LU and Seo, Seong Mi (2017) In Constructive Approximation
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.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Bulk singularity, Fock space, Microscopic density, Two-dimensional eigenvalue ensemble, Ward’s equation
in
Constructive Approximation
pages
35 pages
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
2018-01-07 11:51:51
@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},
  keyword      = {Bulk singularity,Fock space,Microscopic density,Two-dimensional eigenvalue ensemble,Ward’s equation},
  language     = {eng},
  month        = {02},
  pages        = {35},
  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},
  year         = {2017},
}