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25
Multicritical unitary random matrix ensembles and the general Painlevé II equation
, 2008
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Universality of a double scaling limit near singular edge points in random matrix models
, 2008
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A pedestrian’s view on interacting particle systems, KPZ universality, and random matrices
, 2010
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Critical edge behavior in unitary random matrix ensembles and the thirty fourth Painlevé transcendent
, 2008
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Universality for orthogonal and symplectic Laguerretype ensembles
 J. Statist. Phys
, 2007
"... Abstract. We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerretype in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and ..."
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Cited by 16 (0 self)
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Abstract. We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerretype in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and Corollaries 1.2, 1.5, 1.7). They concern the appropriately rescaled kernels Kn,β, correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding results for unitary (β = 2) Laguerretype ensembles have been proved by the fourth author in [23]. The varying weight case at the hard spectral edge
The birth of a cut in unitary random matrix ensembles
 Int Math Res Notices, 2008(article ID rnm166):40
"... We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of eigenvalues is expected in the newborn cut. It t ..."
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We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of eigenvalues is expected in the newborn cut. It turns out that limits of the eigenvalue correlation kernel are given by Hermite kernels corresponding to a finite size Gaussian Unitary Ensemble (GUE). When modifying the double scaling limit slightly, we observe a remarkable transition each time the new cut picks up an additional eigenvalue, leading to a limiting kernel interpolating between GUEkernels for matrices of size k and size k + 1. We prove our results using the RiemannHilbert approach. 1
M.: Random matrix central limit theorems for nonintersecting random
, 2007
"... Abstract We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks a ..."
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Abstract We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the midtime behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.
The RiemannHilbert approach to double scaling limit of random matrix eigenvalues near the ”birth of a cut” transition
, 2007
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Universal behavior for averages of characteristic polynomials at the origin of the spectrum
 Commun.Math.Phys
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