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Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices · Around

2008

Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices

Dean, David S., Majumdar, Satya N.

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We compute exact asymptotic results for the probability of the occurrence of large deviations of the largest (smallest) eigenvalue of random matrices belonging to the Gaussian orthogonal, unitary and symplectic ensembles.

In particular, we show that the probability that all the eigenvalues of an (NxN) random matrix are positive (negative) decreases for large N as ~\exp[-\beta \theta(0) N^2] where the Dyson index \beta characterizes the ensemble and the exponent \theta(0)=(\ln 3)/4=0.274653...
is universal.
We compute the probability that the eigenvalues lie in the interval [\zeta_1,\zeta_2] which allows us to calculate the joint probability distribution of the minimum and the maximum eigenvalue.

Built on

E.P. Wigner, Proc. Cambridge Philos. Soc. 47
1951
Earlier work this paper cites.
F.J. Dyson, J. Math. Phys. 3
1962
Earlier work this paper cites.
R.M. May, Nature, 238
1972
Earlier work this paper cites.
M.L. Mehta, Random Matrices
1991
Earlier work this paper cites.
F.G. Tricomi, Integral Equations
1994
Earlier work this paper cites.
C.A. Tracy and H. Widom, Commun. Math. Phys. 159
1996
Earlier work this paper cites.
J. Baik, P. Deift, and K. Johansson, J. Am. Math. Soc. 12
1999
Earlier work this paper cites.
A. Cavagna, I. Giardina and J.P. Garrahan, Phys. Rev. B, 3960 (2000)
2000
Earlier work this paper cites.

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2005

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J-P. Dedieu and G. Malajovich, arXiv:math/0702360

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While in principle the O ⁡ ( N ) O(N) contributions could have possibly modified this limiting behaviour, the agreement with the Tracy-Widom asymptotics shows that clearly this is not the case

Cited in the paper.

There is clearly a misprint in the sign of exponent of N N given for this fit in AE

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V.A. Osipov and E. Kanzieper, unpublished

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2007

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