Exponential moments for disk counting statistics of random normal matrices in the critical regime
(2023) In Nonlinearity 36(3).- Abstract
We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble, where n is the number of points of the process and m is arbitrary but fixed. We focus on the critical regime where all disk boundaries are merging at speed n − 1 2 , either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large n asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large n asymptotics for n × n determinants with merging planar discontinuities.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/898dddb2-240c-4b93-8671-f3fc4808c6ea
- author
- Charlier, Christophe LU and Lenells, Jonatan LU
- organization
- publishing date
- 2023-03-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- asymptotic analysis, determinants with merging planar discontinuities, moment generating functions, random matrix theory
- in
- Nonlinearity
- volume
- 36
- issue
- 3
- publisher
- London Mathematical Society / IOP Science
- external identifiers
-
- scopus:85147345950
- ISSN
- 0951-7715
- DOI
- 10.1088/1361-6544/acb47c
- language
- English
- LU publication?
- yes
- id
- 898dddb2-240c-4b93-8671-f3fc4808c6ea
- date added to LUP
- 2023-07-03 14:16:30
- date last changed
- 2023-07-03 14:16:30
@article{898dddb2-240c-4b93-8671-f3fc4808c6ea, abstract = {{<p>We obtain large n asymptotics for the m-point moment generating function of the disk counting statistics of the Mittag-Leffler ensemble, where n is the number of points of the process and m is arbitrary but fixed. We focus on the critical regime where all disk boundaries are merging at speed n − 1 2 , either in the bulk or at the edge. As corollaries, we obtain two central limit theorems and precise large n asymptotics of all joint cumulants (such as the covariance) of the disk counting function. Our results can also be seen as large n asymptotics for n × n determinants with merging planar discontinuities.</p>}}, author = {{Charlier, Christophe and Lenells, Jonatan}}, issn = {{0951-7715}}, keywords = {{asymptotic analysis; determinants with merging planar discontinuities; moment generating functions; random matrix theory}}, language = {{eng}}, month = {{03}}, number = {{3}}, publisher = {{London Mathematical Society / IOP Science}}, series = {{Nonlinearity}}, title = {{Exponential moments for disk counting statistics of random normal matrices in the critical regime}}, url = {{http://dx.doi.org/10.1088/1361-6544/acb47c}}, doi = {{10.1088/1361-6544/acb47c}}, volume = {{36}}, year = {{2023}}, }