Fetching the paper…

Reading the bibliography…

Eigenvalue statistics of the real Ginibre ensemble · Around

2007

Eigenvalue statistics of the real Ginibre ensemble

Forrester, Peter J., Nagao, Taro

Original
PDF
Post on X

Understand

The real Ginibre ensemble consists of random $N \times N$ matrices formed from i.i.d.

standard Gaussian entries.
By using the method of skew orthogonal polynomials, the general $n$-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as $n \times n$ Pfaffians with explicit entries.
A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented.

Built on

F.J. Dyson, J. Math. Phys. 3
1962
Earlier work this paper cites.
J. Ginibre, J. Math. Phys. 6
1965
Earlier work this paper cites.
R.M. May, Nature 238
1972
Earlier work this paper cites.
R.E. McMurtrie, J. Theor. Biol. 50
1975
Earlier work this paper cites.
E.R. Smith, J. Phys. A 15
1982
Earlier work this paper cites.
S. Gemam, Ann. Prob. 14
1986
Earlier work this paper cites.
Ph.A. Martin, Rev. Mod. Phys. 60
1988
Earlier work this paper cites.
N. Lehmann and H.-J. Sommers, Phys. Rev. Lett. 67
1991
Earlier work this paper cites.
A. Edelman, E. Kostlan, and M. Shub, J. Amer. Math. Soc. 7
1994
Earlier work this paper cites.

Similar

M.R. Zirnbauer, J. Math. Phys. 37
1996
Cited alongside, same era.
J.H. Hannay, J. Phys. A 29
1996
Cited alongside, same era.
C.W.J. Beenakker, Rev. Mod. Phys. 69
1997
Cited alongside, same era.
K. Efetov, Supersymmetry in disorder and chaos , Cambridge University Press, Cambridge, 1997
1997
Cited alongside, same era.
A. Edelman, J. Multivariate Analysis 60
1997
Cited alongside, same era.
Z.D. Bai, Ann. Prob. 25
1997
Cited alongside, same era.
P. Bleher and X. Di, J. Stat. Phys. 88
Original
1997

Then

J.J.M. Verbaarschot and T. Wettig, Annu. Rev. Nucl. Part. Sci. 50
2000
Later among the works it cites.
F. Haake, Quantum signatures of chaos , 2nd ed., Springer, Berlin, 2000
2000
Later among the works it cites.
M.L. Mehta, Random matrices , 3nd ed., Elsevier, 2004
2004
Later among the works it cites.
E. Kanzieper and G. Akemann, Phys. Rev. Lett. 95
2005
Later among the works it cites.
E. Kanzieper, in Frontiers in Field Theory , ed. O. Kovras, p. 23, Nova Science Publishers, NY (2005)
2005
Later among the works it cites.
D.J. Albers and J.C. Sprott, J. Stat. Phys. 125
2006
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Cited alongside, same era.

P.J. Forrester, Phys. Reports 301

1998

Cited alongside, same era.

P.J. Forrester and G. Honner, J. Phys. A 32

1999

Cited alongside, same era.

P.J. Forrester, Log-gases and Random Matrices , www.ms.unimelb.edu.au/˜matpjf/matpjf.html

Cited in the paper.

G. Akemann and E. Kanzieper, preprint arXiv:math-ph/0703019v2

Cited in the paper.

J. Feng, V. Jirsa, and M. Ding, Chaos 16

2006

Later among the works it cites.

K. Rajan and L.F. Abbott, Phys. Rev. Lett. 97

2006

Later among the works it cites.

C.D. Sinclair, preprint arXiv:math-ph/0605006 (2006)

2006

Later among the works it cites.