2022/12/01 by Thomas Bothner, Bothner, Thomas, Alex Little +1 · 2 citations
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Advanced Algebra and Geometry #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2212.00525
We show that the distribution of bulk spacings between pairs of adjacent eigenvalue real parts of a random matrix drawn from the complex elliptic Ginibre ensemble is asymptotically given by a generalization of the Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same generalization is expressed in terms of an integro-differential Painlevé function and it is shown that the generalized Gaudin-Mehta distribution describes the crossover, with increasing degree of non-Hermiticity, from Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex Ginibre Ensemble.