Gap Universality of Generalized Wigner and beta-Ensembles

Wigner, E.: Characteristic vectors of bordered matrices with infinite dimensions. Ann. of Math

1955

Earlier work this paper cites.

Dyson, F.J.: A Brownian-motion model for the eigenvalues of a random matrix. J. Math. Phys

1962

Earlier work this paper cites.

Mehta, M.L.: Random Matrices. Academic Press, New York, 1991

1991

Earlier work this paper cites.

Ogawa, T.; Ozawa, T.: Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger mixed problem. J. Math. Anal. Appl

1991

Earlier work this paper cites.

Fokas, A. S.; Its, A. R.; Kitaev, A. V.: The isomonodromy approach to matrix models in 2 2 D quantum gravity. Comm. Math. Phys

1992

Earlier work this paper cites.

Helffer, B., Sjöstrand, J.: On the correlation for Kac-like models in the convex case. J. Statis. Phys

1994

Earlier work this paper cites.

Tracy, C., Widom, H.: Level spacing distributions and the Airy kernel. Commun. Math. Phys

1994

Earlier work this paper cites.

Boutet de Monvel, A., Pastur, L., Shcherbina, M.: On the statistical mechanics approach in the Random Matrix Theory. Integrated Density of States. J. Stat. Phys

1995

Earlier work this paper cites.

Tracy, C., Widom, H.: On orthogonal and symplectic matrix ensembles, Comm. Math. Phys

1996

Earlier work this paper cites.

Naddaf, A., Spencer, T.: On homogenization and scaling limit of some gradient perturbations of a massless free field, Commun. Math. Phys

1997

Earlier work this paper cites.

Pastur, L., Shcherbina, M.: Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles. J. Stat. Phys

1997

Earlier work this paper cites.

Bleher, P., Its, A.: Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math

1999

Earlier work this paper cites.

Deift, P.: Orthogonal polynomials and random matrices: a Riemann-Hilbert approach. Courant Lecture Notes in Mathematics

1999

Earlier work this paper cites.

Deift, P., Kriecherbauer, T., McLaughlin, K.T-R, Venakides, S., Zhou, X.: Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory. Comm. Pure Appl. Math

1999

Earlier work this paper cites.

Deift, P., Kriecherbauer, T., McLaughlin, K.T-R, Venakides, S., Zhou, X.: Strong asymptotics of orthogonal polynomials with respect to exponential weights. Comm. Pure Appl. Math

1999

Earlier work this paper cites.

Widom H.: On the relation between orthogonal, symplectic and unitary matrix ensembles. J. Statist. Phys

1999

Earlier work this paper cites.

Deuschel, J.-D., Giacomin, G., Ioffe, D.: Large deviations and concentration properties for ∇ φ \nabla\varphi interface models. Probab. Th. Relat. Fields

2000

Earlier work this paper cites.

Albeverio, S., Pastur, L., Shcherbina, M.: On the 1 / n 1/n expansion for some unitary invariant ensembles of random matrices, Commun. Math. Phys

2001

Earlier work this paper cites.

Giacomin, G., Olla, S., Spohn, H.: Equilibrium fluctuations for ∇ φ \nabla\varphi interface model. Ann. Probab

2001

Cited alongside, same era.

Johansson, K.: Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices. Comm. Math. Phys

2001

Cited alongside, same era.

Dumitriu, I., Edelman, A.: Matrix models for beta ensembles. J. Math. Phys

2002

Cited alongside, same era.

Helffer, B.: Semiclassical Analysis, Witten Laplacians and Statistical Mechanics, Series on Partial Differential Equations and Applications

2002

Cited alongside, same era.

Bach, V.: Moller, J.-S.: Correlation at low temperature. I. Exponential decay. J. Funct. Anal

2003

Cited alongside, same era.

Valkó, B.; Virág, B.: Large gaps between random eigenvalues. Ann. Probab

2010

Later among the works it cites.

Caffarelli, L., Chan, C.H., Vasseur, A.: Regularity theory for parabolic nonlinear integral operators, J. Amer. Math. Soc

2011

Later among the works it cites.

Erdős, L., Schlein, B., Yau, H.-T.: Universality of Random Matrices and Local Relaxation Flow. Invent. Math. 185

2011

Later among the works it cites.

Erdős, L., Yau, H.-T., Yin, J.: Universality for generalized Wigner matrices with Bernoulli distribution

2011

Later among the works it cites.

Erdős, L., Yau, H.-T., Yin, J.: Universality for generalized Wigner matrices with Bernoulli distribution. J. of Combinatorics

2011

Later among the works it cites.