Journal article icon

Journal article

A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions

Abstract:

We establish a representation of the joint moments of the characteristic polynomial of a CUE random matrix and its derivative in terms of a solution of the -Painlev´e V equation. The derivation involves the analysis of a formula for the joint moments in terms of a determinant of generalised Laguerre polynomials using the Riemann-Hilbert method. We use this connection with the -Painlev´e V equation to derive explicit formulae for the joint moments and to show that in the large-matrix limit the...

Expand abstract
Publication status:
Published
Peer review status:
Peer reviewed

Actions


Access Document


Publisher copy:
10.1088/1361-6544/ab28c7

Authors


More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Queens College
Role:
Author
Publisher:
IOP Science
Journal:
Nonlinearity More from this journal
Volume:
32
Issue:
2019
Pages:
4033-4078
Publication date:
2019-09-13
Acceptance date:
2019-06-11
DOI:
EISSN:
1361-6544
ISSN:
0951-7715
Keywords:
Pubs id:
pubs:1055642
UUID:
uuid:084b42e1-9433-4bf5-b3ae-ad356112a4c6
Local pid:
pubs:1055642
Source identifiers:
1055642
Deposit date:
2019-09-25

Terms of use


Views and Downloads






If you are the owner of this record, you can report an update to it here: Report update to this record

TO TOP