Eigenvalue statistics of the real Ginibre ensemble.

  title={Eigenvalue statistics of the real Ginibre ensemble.},
  author={Peter J. Forrester and Taro Nagao},
  journal={Physical review letters},
  volume={99 5},
The real Ginibre ensemble consists of random N x N matrices formed from independent and identically distributed 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 x n Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis… 

Tables from this paper

Extremal laws for the real Ginibre ensemble
The real Ginibre ensemble refers to the family of n n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately
General eigenvalue correlations for the real Ginibre ensemble
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
The Ginibre evolution in the large-N limit
We analyse statistics of the real eigenvalues of gl(N,R)-valued Brownian motion (the 'Ginibre evolution') in the limit of large $N$. In particular, we calculate the limiting two-time correlation
Characteristic polynomials in real Ginibre ensembles
We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a
Edge Distribution of Thinned Real Eigenvalues in the Real Ginibre Ensemble
This paper is concerned with the explicit computation of the limiting distribution function of the largest real eigenvalue in the real Ginibre ensemble when each real eigenvalue has been removed
The Ginibre Ensemble of Real Random Matrices and its Scaling Limits
We give a closed form for the correlation functions of ensembles of a class of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a 2 × 2 matrix kernel
Real spectra of large real asymmetric random matrices.
  • W. Tarnowski
  • Mathematics, Computer Science
    Physical review. E
  • 2022
It is shown that in the limit of large matrix size the density of real eigenvalues is proportional to the square root of the asymptotic density of complex eigen values continuated to the real line.
Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble
The partly symmetric real Ginibre ensemble consists of matrices formed as linear combinations of real symmetric and real anti-symmetric Gaussian random matrices. Such matrices typically have both
Integrable Structure of Ginibre’s Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
Abstract In the recent publication (E. Kanzieper and G. Akemann in Phys. Rev. Lett. 95:230201, 2005), an exact solution was reported for the probability pn,k to find exactly k real eigenvalues in the
Directional Extremal Statistics for Ginibre Eigenvalues
We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel


Quantum signatures of chaos
The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Random Matrices
This workshop was unusually diverse, even by MSRI standards; the attendees included analysts, physicists, number theorists, probabilists, combinatorialists, and more.
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
  • Rev. Lett. 95, 230201
  • 2005
  • 6 , 440
  • 1965
  • Rev. Lett. 67, 941
  • 1991
Supersymmetry in disorder and chaos
A 15
  • 1982
  • Mod. Phys. 69, 731
  • 1997