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Asymptotics for the Fredholm determinant of the sine kernel on a union of intervals
 Commun. Math. Phys
, 1995
"... The sine kernel ..."
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
ON THE OCCURRENCE OF THE SINE KERNEL IN CONNECTION WITH THE SHIFTED MOMENTS OF THE RIEMANN ZETA FUNCTION
, 2008
"... We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture that the ..."
Abstract

Cited by 5 (0 self)
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We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture
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 ..."
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 ..."
Abstract

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 &
Results 1  10
of
90