Finite size corrections for real eigenvalues of the elliptic Ginibre matrices

Abstract

We consider the elliptic Ginibre matrices in the orthogonal symmetry class that interpolates between the real Ginibre ensemble and the Gaussian orthogonal ensemble. We obtain the finite size corrections of the real eigenvalue densities in both the global and edge scaling regimes, as well as in both the strong and weak non-Hermiticity regimes. Our results extend and provide the rate of convergence to the previous recent findings in the aforementioned limits. In particular, in the Hermitian limit, our results recover the finite size corrections of the Gaussian orthogonal ensemble established by Forrester, Frankel and Garoni.

arXiv comment27 pages, 3 figures

References in corpus (36)

• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• Eigenvalue statistics of the real Ginibre ensemble
• Directed Quantum Chaos
• Almost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
• The Ginibre ensemble of real random matrices and its scaling limits
• Nonlinear Analogue of the May-Wigner Instability Transition
• Noninteracting fermions in a trap and random matrix theory
• Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble
• Integrable Structure of Ginibre's Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
• Edge scaling limits for a family of non-Hermitian random matrix ensembles
• Pfaffian formulae for one dimensional coalescing and annihilating systems
• Wigner-Poisson statistics of topological transitions in a Josephson junction
• Fast approach to the Tracy-Widom law at the edge of GOE and GUE
• Asymptotic corrections to the eigenvalue density of the GUE and LUE
• Universality at weak and strong non-Hermiticity beyond the elliptic Ginibre ensemble
• Counting statistics for non-interacting fermions in a $d$-dimensional potential
• Asymptotic form of the density profile for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry
• Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation
• Fine asymptotic behavior in eigenvalues of random normal matrices: Ellipse Case
• Topology trivialization transition in random non-gradient autonomous ODE's on a sphere
• Finite N corrections to the limiting distribution of the smallest eigenvalue of Wishart complex matrices
• Condition numbers for real eigenvalues in the real Elliptic Gaussian ensemble
• A method to calculate correlation functions for $\beta =1$ random matrices of odd size
• The Elliptic Ginibre Ensemble: A Unifying Approach to Local and Global Statistics for Higher Dimensions
• Counting statistics for non-interacting fermions in a rotating trap
• The Interpolating Airy Kernels for the beta=1 and beta=4 Elliptic Ginibre Ensembles
• Universal Wide Correlators in Non-Gaussian Orthogonal, Unitary and Symplectic Random Matrix Ensembles
• Universal scaling limits of the symplectic elliptic Ginibre ensemble
• A note on the expansion of the smallest eigenvalue distribution of the LUE at the hard edge
• What is the probability that a large random matrix has no real eigenvalues?
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• On the number of real eigenvalues of a product of truncated orthogonal random matrices
• Rate of Convergence to the Circular Law via Smoothing Inequalities for Log-Potentials
• A Stirling-type formula for the distribution of the length of longest increasing subsequences
• Wronskian structures of planar symplectic ensembles
• Edge Behavior of Higher Complex-Dimensional Determinantal Point Processes

Cited by in corpus (3)

• Condition numbers for real eigenvalues of real elliptic ensemble: weak non-normality at the edge
• Asymptotic Expansions of Gaussian and Laguerre Ensembles at the Soft Edge II: Level Densities
• The probability of almost all eigenvalues being real for the elliptic real Ginibre ensemble