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LevelSpacing Distributions and the Airy Kernel
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Scaling levelspacing distribution functions in the "bulk of the spectrum" in random matrix models of N x N hermitian matrices and then going to the limit N — » oo leads to the Fredholm determinant of the sine kernel sinπ(x — y)/π(x — y). Similarly a scaling limit at the "edge o ..."
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Cited by 430 (24 self)
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Scaling levelspacing distribution functions in the "bulk of the spectrum" in random matrix models of N x N hermitian matrices and then going to the limit N — » oo leads to the Fredholm determinant of the sine kernel sinπ(x — y)/π(x — y). Similarly a scaling limit at the &
ITD 92/93–11 LevelSpacing Distributions and the Airy Kernel
, 1992
"... Scaling levelspacing distribution functions in the “bulk of the spectrum ” in random matrix models of N ×N hermitian matrices and then going to the limit N → ∞, leads to the Fredholm determinant of the sine kernel sin π(x − y)/π(x − y). Similarly a double scaling limit at the “edge of the spectrum ..."
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Scaling levelspacing distribution functions in the “bulk of the spectrum ” in random matrix models of N ×N hermitian matrices and then going to the limit N → ∞, leads to the Fredholm determinant of the sine kernel sin π(x − y)/π(x − y). Similarly a double scaling limit at the “edge of the spectrum
THE RIEMANN ZETAFUNCTION AND THE SINE KERNEL
, 2008
"... We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zetafunction along the critical line. We establish this occurrence rigorously for the shifted second moment and, under some constraints on the shifts, for the shifted fourth moment. Our ..."
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We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zetafunction along the critical line. We establish this occurrence rigorously for the shifted second moment and, under some constraints on the shifts, for the shifted fourth moment. Our
FROM SINE KERNEL TO POISSON STATISTICS
"... Abstract. We study the Sineβ process introduced in [B. Valko ́ and B. Virág. Invent. math. 177 463508 (2009)] when the inverse temperature β tends to 0. This point process has been shown to be the scaling limit of the eigenvalues point process in the bulk of βensembles and its law is characterize ..."
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Abstract. We study the Sineβ process introduced in [B. Valko ́ and B. Virág. Invent. math. 177 463508 (2009)] when the inverse temperature β tends to 0. This point process has been shown to be the scaling limit of the eigenvalues point process in the bulk of βensembles and its law is characterized in terms of the winding numbers of the Brownian carrousel at different angular speeds. After a careful analysis of this family of coupled diffusion processes, we prove that the Sineβ point process converges weakly to a Poisson point process on R. Thus, the Sineβ point processes establish a smooth crossover between the rigid clock (or picket fence) process (corresponding to β =∞) and the Poisson process. 1. Introduction and
Universality of sinekernel for Wigner matrices with a small Gaussian perturbation
, 2009
"... We consider N × N Hermitian random matrices with independent identically distributed entries (Wigner matrices). We assume that the distribution of the entries have a Gaussian component with variance N −3/4+β for some positive β> 0. We prove that the local eigenvalue statistics follows the univers ..."
Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals
 Commun. Math. Phys
, 1995
"... The sine kernel ..."
Local Sine and Cosine Bases of Coifman and Meyer and the Construction of Smooth Wavelets
 in Wavelets: A Tutorial in Theory and Applications
, 1991
"... . We give a detailed account of the local cosine and sine bases of Coifman and Meyer. We describe some of their applications; in particular, based on an approach by Coifman and Meyer, we show how these local bases can be used to obtain arbitrarily smooth wavelets. The understanding of this material ..."
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Cited by 75 (5 self)
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. We give a detailed account of the local cosine and sine bases of Coifman and Meyer. We describe some of their applications; in particular, based on an approach by Coifman and Meyer, we show how these local bases can be used to obtain arbitrarily smooth wavelets. The understanding of this material
Fredholm Determinants, Differential Equations and Matrix Models
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the und ..."
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Cited by 142 (20 self)
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as φ and φ satisfy a certain type of differentiation formula. The (φ, φ) pairs for the sine, Airy, and Bessel kernels satisfy such relations, as do the pairs which arise in the finite N Hermite, Laguerre and Jacobi ensembles and in matrix models of 2D quantum gravity. Therefore we shall be able
Results 1  10
of
355