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Based on the exact relationship to random matrix theory, we present analternative method of evaluating the probability distribution of the k-thsmallest Dirac eigenvalue in the epsilon-regime of QCD and QCD-like theories.By utilizing the Nystrom-type discretization of Fredholm determinants andPfaffians, practical trouble of evaluating multiple integrations iscircumvented and technical restrictions on the parities of the number offlavors and of the topological charge present in our previous treatment forbeta=1 and 4 cases [Phys. Rev. D 63, 045012 (2001)] are partly lifted. Thismethod is also applied to the distributions of spacings between k-thnearest-neighboring levels in the mobility edges of Anderson Hamiltonian andDirac operator in high-temperature QCD.

Distribution of the k-th smallest Dirac operator eigenvalue : an update