TL;DR
This paper derives an exponential approximation formula for the distribution of complex spacing ratios in the Ginibre ensemble, aiding the analysis of eigenvalue correlations in non-Hermitian systems.
Contribution
It provides the first analytical approximation for the distribution of complex spacing ratios in the Ginibre ensemble, including moments, with exponential convergence.
Findings
Approximation formula converges exponentially fast to the large-size limit.
Derived moments of the distribution in the infinite matrix size limit.
Provides analytical tools for studying eigenvalue correlations in non-Hermitian systems.
Abstract
Recently, S\'a, Ribeiro and Prosen introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.
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