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...
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- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Authors
Bibliographic Details
- Publisher:
- IOP Science Publisher's website
- Journal:
- Nonlinearity Journal website
- Volume:
- 32
- Issue:
- 2019
- Pages:
- 4033-4078
- Publication date:
- 2019-09-13
- Acceptance date:
- 2019-06-11
- DOI:
- EISSN:
-
1361-6544
- ISSN:
-
0951-7715
Item Description
- 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
- Copyright date:
- 2019
- Notes:
- © 2019 IOP Publishing Ltd and London Mathematical Society. This is the accepted manuscript version of the article. The final version is available from IOP Science at: https://doi.org/10.1088/1361-6544/ab28c7
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