A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions
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...
| Main Authors: | , , , , , , |
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| Format: | Journal article |
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IOP Science
2019
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| _version_ | 1826257991538573312 |
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| author | Keating, J Basor, E Bleher, P Buckingham, R Grava, T Its, A Its, E |
| author_facet | Keating, J Basor, E Bleher, P Buckingham, R Grava, T Its, A Its, E |
| author_sort | Keating, J |
| collection | OXFORD |
| description | 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 joint moments are related to a solution of the -Painlev´e III0 equation. Using the conformal block expansion of the ⌧ -functions associated with the -Painlev´e V and the -Painlev´e III0 equations leads to general conjectures for the joint moments. |
| first_indexed | 2024-03-06T18:26:57Z |
| format | Journal article |
| id | oxford-uuid:084b42e1-9433-4bf5-b3ae-ad356112a4c6 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:26:57Z |
| publishDate | 2019 |
| publisher | IOP Science |
| record_format | dspace |
| spelling | oxford-uuid:084b42e1-9433-4bf5-b3ae-ad356112a4c62022-03-26T09:12:08ZA representation of joint moments of CUE characteristic polynomials in terms of Painlevé functionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:084b42e1-9433-4bf5-b3ae-ad356112a4c6Symplectic Elements at OxfordIOP Science2019Keating, JBasor, EBleher, PBuckingham, RGrava, TIts, AIts, EWe 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 joint moments are related to a solution of the -Painlev´e III0 equation. Using the conformal block expansion of the ⌧ -functions associated with the -Painlev´e V and the -Painlev´e III0 equations leads to general conjectures for the joint moments. |
| spellingShingle | Keating, J Basor, E Bleher, P Buckingham, R Grava, T Its, A Its, E A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title_full | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title_fullStr | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title_full_unstemmed | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title_short | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions |
| title_sort | representation of joint moments of cue characteristic polynomials in terms of painleve functions |
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