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Exponential moments for disk counting statistics of random normal matrices in the critical regime

Charlier, Christophe LU and Lenells, Jonatan LU (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.

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author
and
organization
publishing date
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}},
}