On Bulk Singularities in the Random Normal Matrix Model
(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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https://lup.lub.lu.se/record/ea10ad32-fbd6-4ae9-a16f-0d4876c41b5b
- author
- Ameur, Yacin LU and Seo, Seong Mi
- organization
- publishing date
- 2018-02
- 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}}, }