The Random Normal Matrix Model : Insertion of a Point Charge
(2021) In Potential Analysis 2021.- Abstract
- In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits (“Mittag-Leffler fields”) and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log|pn(ζ)| where pn is the characteristic polynomial of an n:th order random normal matrix.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/28f04de6-7967-4682-aaa8-1d6f814dd2ec
- author
- Ameur, Yacin LU ; Kang, Nam-Gyu and Seo, Seong-Mi
- organization
- publishing date
- 2021-08-05
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Planar Coulomb gas, Microscopic limit, Conical limit, Fock-Sobolev space, Ward's equation
- in
- Potential Analysis
- volume
- 2021
- pages
- 42 pages
- publisher
- Springer
- external identifiers
-
- scopus:85111796183
- ISSN
- 1572-929X
- DOI
- 10.1007/s11118-021-09942-z
- language
- English
- LU publication?
- yes
- id
- 28f04de6-7967-4682-aaa8-1d6f814dd2ec
- date added to LUP
- 2021-12-15 17:04:02
- date last changed
- 2022-04-27 06:44:14
@article{28f04de6-7967-4682-aaa8-1d6f814dd2ec, abstract = {{In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits (“Mittag-Leffler fields”) and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log|pn(ζ)| where pn is the characteristic polynomial of an n:th order random normal matrix.}}, author = {{Ameur, Yacin and Kang, Nam-Gyu and Seo, Seong-Mi}}, issn = {{1572-929X}}, keywords = {{Planar Coulomb gas; Microscopic limit; Conical limit; Fock-Sobolev space; Ward's equation}}, language = {{eng}}, month = {{08}}, publisher = {{Springer}}, series = {{Potential Analysis}}, title = {{The Random Normal Matrix Model : Insertion of a Point Charge}}, url = {{http://dx.doi.org/10.1007/s11118-021-09942-z}}, doi = {{10.1007/s11118-021-09942-z}}, volume = {{2021}}, year = {{2021}}, }