τ-function of discrete isomonodromy transformations and probability

Author:

Arinkin D.,Borodin A.

Abstract

AbstractWe introduce theτ-function of a difference rational connection (d-connection) and its isomonodromy transformations. We show that in a continuous limit ourτ-function agrees with the Jimbo–Miwa–Uenoτ-function. We compute theτ-function for the isomonodromy transformations leading to difference Painlevé V and difference Painlevé VI equations. We prove that the gap probability for a wide class of discrete random matrix type models can be viewed as theτ-function for an associated d-connection.

Publisher

Wiley

Subject

Algebra and Number Theory

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Gap probabilities in the Laguerre unitary ensemble and discrete Painlevé equations;Journal of Physics A: Mathematical and Theoretical;2020-08-18

2. $q$ -Racah Ensemble and Discrete Painlevé Equation;International Mathematics Research Notices;2019-11-05

3. Moduli Spaces ofq-Connections and Gap Probabilities;International Mathematics Research Notices;2016-01-05

4. Noncommutative geometry and Painlevé equations;Algebra & Number Theory;2015-09-07

5. Semiclassical orthogonal polynomial systems on nonuniform lattices, deformations of the Askey table, and analogues of isomonodromy;Nagoya Mathematical Journal;2015-09

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