Tau-function of discrete isomonodromy transformations and probability

Abstract

We introduce the tau-function of a rational d-connection and its isomonodromy transformations. We show that in a continuous limit our tau-function agrees with the Jimbo-Miwa-Ueno tau-function, compute the tau-function for the isomonodromy transformations leading to difference Painleve V and difference Painleve VI equations, and prove that the gap probability for a wide class of discrete random matrix type models can be viewed as the tau-function for an associated d-connection.

26 pages

References in corpus (4)

• Application of the $\tau$-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE
• Distribution of the first particle in discrete orthogonal polynomial ensembles
• Discrete Painlevé equations and random matrix averages
• A unified description of the asymmetric q-P_{v} and d-P_{iv} equations and their Schlesinger transformations

Cited by in corpus (5)

• Gap Probabilities in the Laguerre Unitary Ensemble and Discrete Painlevé Equations
• Noncommutative geometry and Painlevé equations
• Factorizations of Rational Matrix Functions with Application to Discrete Isomonodromic Transformations and Difference Painlevé Equations
• Recurrence relations for the generalized Laguerre and Charlier orthogonal polynomials and discrete Painlevé equations on the $D_6^{(1)}$ Sakai surface
• Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials