Advanced

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.

Please use this url to cite or link to this publication:
author
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
2018-05-29 09:18:23
@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},
  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},
  volume       = {47},
  year         = {2018},
}