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math.CO2000
Integrable Lattices: Random Matrices and Random Permutations
Pierre van Moerbeke
These lectures present a survey of recent developments in the area of random matrices (finite and infinite) and random permutations. These probabilistic problems suggest matrix int…
nlin.SI2000
Darboux transforms on Band Matrices, Weights and associated Polynomials
Mark Adler, Pierre van Moerbeke
Classically, it is well known that a single weight on a real interval leads to orthogonal polynomials. In "Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert probl…
math-ph2000
Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum
Mark Adler, Pierre van Moerbeke
Given the Hermitian, symmetric and symplectic ensembles, it is shown that the probability that the spectrum belongs to one or several intervals satisfies a nonlinear PDE. This is d…