Approximation formula for complex spacing ratios in the Ginibre ensemble

Abstract

Recently, Sá, 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.

reference added, version published in Phys. Rev. E

References in corpus (4)

• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Universal Signature from Integrability to Chaos in Dissipative Open Quantum Systems