The complex elliptic Ginibre ensemble at weak non-Hermiticity: bulk spacing distributions
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL(2024)
Abstract
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 Painlev & eacute; 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.
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Key words
complex elliptic Ginibre ensemble,fredholm determinants,Gaudin-Mehta gap statistics,integro-differential Painlev & eacute,functions,Gaudin-Mehta and Poisson gap distribution.
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