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Differential Equations for Approximate Solutions of Painlevé Equations: Application to the Algebraic Solutions of the Painlevé-III Equation
Robert J. Buckingham, Peter D. Miller
It is well known that the Painlevé equations can formally degenerate to autonomous differential equations with elliptic function solutions in suitable scaling limits. A way to make…
On the algebraic solutions of the Painleve-III (D7) equation
Robert J. Buckingham, Peter D. Miller
The D7 degeneration of the Painleve-III equation has solutions that are rational functions of for certain parameter values. We apply the isomonodromy method to obtain a R…
A representation of joint moments of CUE characteristic polynomials in terms of Painleve functions
Estelle Basor, Pavel Bleher, Robert Buckingham +4
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 sigma-Painleve V equatio…
Large-degree asymptotics of rational Painleve-IV functions associated to generalized Hermite polynomials
Robert Buckingham
The Painleve-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers m and n. These f…
Large deformations of the Tracy-Widom distribution I. Non-oscillatory asymptotics
Thomas Bothner, Robert Buckingham
We analyze the left-tail asymptotics of deformed Tracy-Widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random matrix ensembles after…
Semiclassical soliton ensembles for the three-wave resonant interaction equations
Robert J. Buckingham, Robert M. Jenkins, Peter D. Miller
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amp…