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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 &
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 sinπ(x − y)/π(x − y). Similarly a scaling limit at the “edge of the spectrum ” leads ..."
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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 sinπ(x − y)/π(x − y). Similarly a scaling limit at the “edge of the spectrum
Level Spacing Distributions and the Bessel Kernel
 MATHEMATICAL PHYSICS
, 1994
"... Scaling models of random N x N hermitian matrices and passing to the limit N » oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others ' a ..."
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Cited by 54 (1 self)
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Scaling models of random N x N hermitian matrices and passing to the limit N » oo leads to integral operators whose Fredholm determinants describe the statistics of the spacing of the eigenvalues of hermitian matrices of large order. For the Gaussian Unitary Ensemble, and for many others &apos
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
Asymptotic level spacing distribution for a qdeformed random matrix ensemble
 J. Phys. A: Math. Gen
, 1996
"... Abstract. We obtain the asymptotic behaviour of the nearestneighbour level spacing distribution for a qdeformed unitary random matrix ensemble. The qdeformed unitary random matrix ensemble introduced in [1] describes a transition in spectral statistics from the highly correlated Gaussian unitary ..."
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Cited by 1 (1 self)
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Abstract. We obtain the asymptotic behaviour of the nearestneighbour level spacing distribution for a qdeformed unitary random matrix ensemble. The qdeformed unitary random matrix ensemble introduced in [1] describes a transition in spectral statistics from the highly correlated Gaussian unitary
Critical level spacing distribution of twodimensional disordered systems with spinorbit
, 1995
"... coupling ..."
HigherOrder Energy Level Spacing Distributions in the Transition Region Between Regularity and Chaos
, 1998
"... . We study general energy level spacing distributions of Hamiltonian systems in the transition region between regularity and chaos. The well known Brody distribution, which results from a powerlaw ansatz for the levelrepulsion function, describes the nearestneighbour spectral spacings. We pursue ..."
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. We study general energy level spacing distributions of Hamiltonian systems in the transition region between regularity and chaos. The well known Brody distribution, which results from a powerlaw ansatz for the levelrepulsion function, describes the nearestneighbour spectral spacings. We pursue
GTP986 Correspondence between classical dynamics and energy level spacing distribution in the transition billiard systems
, 1998
"... The Robnik billiard is investigated in detail both classically and quantally in the transition range from integrable to almost chaotic system. We find out that a remarkable correspondence between characteristic features of classical dynamics, especially topological structure of integrable regions in ..."
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in the Poincaré surface of section, and the statistics of energy level spacings appears with a system parameter λ being varied. It is shown that the variance of the level spacing distribution changes its behavior at every particular values of λ in such a way that classical dynamics changes its topological
Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model
, 1994
"... Abstract We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function P(s). We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues ..."
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Abstract We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function P(s). We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues
Results 1  10
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4,244