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17
Multicritical unitary random matrix ensembles and the general Painlevé II equation
, 2008
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Lectures on random matrix models. The RiemannHilbert approach
, 2008
"... This is a review of the RiemannHilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the RiemannHilbert approach to the large N asymptotics of orthogonal polynomials and its appli ..."
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This is a review of the RiemannHilbert approach to the large N asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the RiemannHilbert approach to the large N asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the large N asymptotics of the partition function, and random matrix models with external source.
The RiemannHilbert approach to double scaling limit of random matrix eigenvalues near the ”birth of a cut” transition
, 2007
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Asymptotics of HermitePadé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)
, 2007
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Painlevé II in random matrix theory and related fields. arXiv:1210.3381
, 2012
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4 GLOBAL ASYMPTOTICS FOR THE CHRISTOFFELDARBOUX KERNEL OF RANDOM MATRIX THEORY
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UNIVERSALITY IN UNITARY RANDOM MATRIX ENSEMBLES WHEN THE SOFT EDGE MEETS THE
, 2007
"... Dedicated to Percy Deift on the occasion of his sixtieth birthday Abstract. Unitary random matrix ensembles Z −1 n,N (detM)α exp(−N Tr V (M))dM defined on positive definite matrices M, where α> −1 and V is real analytic, have a hard edge at 0. The equilibrium measure associated with V typically v ..."
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Dedicated to Percy Deift on the occasion of his sixtieth birthday Abstract. Unitary random matrix ensembles Z −1 n,N (detM)α exp(−N Tr V (M))dM defined on positive definite matrices M, where α> −1 and V is real analytic, have a hard edge at 0. The equilibrium measure associated with V typically vanishes like a square root at soft edges of the spectrum. For the case that the equilibrium measure vanishes like a square root at 0, we determine the scaling limits of the eigenvalue correlation kernel near 0 in the limit when n, N → ∞ such that n/N −1 = O(n −2/3). For each value of α> −1 we find a oneparameter family of limiting kernels that we describe in terms of the HastingsMcLeod solution of the Painlevé II equation with parameter α + 1/2.