Fetching the paper…

Reading the bibliography…

2008

General Eigenvalue Correlations for the Real Ginibre Ensemble

Sommers, Hans-Jürgen, Wieczorek, Waldemar

Original
PDF
Post on X

Understand

We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian generating functional for $n$-point densities.

This produces a simple free-fermion diagram expansion for the correlations leading to quaternion determinants in each order n.
All will explicitly be given with the help of a very simple symplectic kernel for even dimension $N$.
The kernel is valid both for complex and real eigenvalues and describes a deep connection between both.

General Eigenvalue Correlations for the Real Ginibre Ensemble · Around

Built on

J.Ginibre, J. Math. Phys. 6
1965
Earlier work this paper cites.
R.M.May, Nature 298
1972
Earlier work this paper cites.
H.Sompolinsky, A.Crisanti and H.-J.Sommers, Phys. Rev. Lett. 61
1988
Earlier work this paper cites.
N.Lehmann and H.-J. Sommers, Phys. Rev. Lett. 67
1991
Earlier work this paper cites.

Similar

A.Edelman, E.Kostlan and M.Shub, J. Amer. Math. Soc. 7
1994
Cited alongside, same era.
A.Edelman, J. Multivariate Anal. 60
1997
Cited alongside, same era.
K.B.Efetov, Phys. Rev. Lett. 79
1997
Cited alongside, same era.
C.D.Sinclair, arXiv: math-ph/0605006 (2006)
2006
Cited alongside, same era.
A.Borodin, C.D.Sinclair, arXiv: math-ph/0706.2670v2
Cited in the paper.
W.Bruzda, V.Cappelini, H.-J.Sommers, K.Życzkowski, arXiv: quant-ph/0804.2361
Original
Cited in the paper.

Then

J.Kwapien, S. Drozdz, A.Z. Gorski and F. Oswiecimka, Acta Phys. Pol. B37
2006
Later among the works it cites.
H.-J. Sommers, J. Phys. A 40
2007
Later among the works it cites.
G. Akemann and E.Kanzieper, J. Stat. Phys. 129
2007
Later among the works it cites.
P.J.Forrester and T. Nagao, Phys. Rev. Lett. 99
2007
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…