A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions
dc.contributor.author | Basor, Estelle | |
dc.contributor.author | Bleher, Pavel | |
dc.contributor.author | Buckingham, Robert | |
dc.contributor.author | Grava, Tamara | |
dc.contributor.author | Its, Alexander | |
dc.contributor.author | Its, Elizabeth | |
dc.contributor.author | Keating, Jonathan P. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2020-08-28T19:05:18Z | |
dc.date.available | 2020-08-28T19:05:18Z | |
dc.date.issued | 2019-10 | |
dc.description.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 -Painlevé 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 -Painlevé 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 -Painlevé III equation. Using the conformal block expansion of the -functions associated with the -Painlevé V and the -Painlevé III equations leads to general conjectures for the joint moments. | en_US |
dc.eprint.version | Author's manuscript | en_US |
dc.identifier.citation | Basor, E., Bleher, P., Buckingham, R., Grava, T., Its, A., Its, E., & Keating, J. P. (2019). A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions. Nonlinearity, 32(10), 4033–4078. https://doi.org/10.1088/1361-6544/ab28c7 | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/23728 | |
dc.language.iso | en | en_US |
dc.publisher | IOP | en_US |
dc.relation.isversionof | 10.1088/1361-6544/ab28c7 | en_US |
dc.relation.journal | Nonlinearity | en_US |
dc.rights | Publisher Policy | en_US |
dc.source | ArXiv | en_US |
dc.subject | joint moments | en_US |
dc.subject | CUE random matrix | en_US |
dc.subject | Painlevé functions | en_US |
dc.title | A representation of joint moments of CUE characteristic polynomials in terms of Painlevé functions | en_US |
dc.type | Article | en_US |