Exponential moments for disk counting statistics of random normal matrices in the critical regime. (1st March 2023)

• Record Type: Journal Article
• Authors: Charlier, Christophe; Lenells, Jonatan
• Is Part Of: Nonlinearity. Volume 36:Number 3(2023)
• Page Start: 1593
• Page End: 1616
• Publication Date: 2023-03-01
• Subjects: determinants with merging planar discontinuities -- moment generating functions -- random matrix theory -- asymptotic analysis; 41A60 -- 60B20 -- 60G55; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/acb47c
• Languages: English
• ISSNs: 0951-7715

Abstract

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.