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arXiv · 1507.08830

Gap probabilities and densities of extreme eigenvalues of random matrices: Exact results

Santosh Kumar
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Abstract

We derive exact results for gap probabilities, as well as densities of extreme eigenvalues for six complex random matrix ensembles of fundamental importance. These are Gauss-Wigner, Laguerre-Wishart, Cauchy-Lorentz (two variants), Jacobi-MANOVA and Bures-Hall (trace unrestricted). We deal with both correlated and uncorrelated cases. Extensive Monte-Carlo simulations based on explicit matrix models or Dyson's log-gas formalism have also been performed, which corroborate all analytical results.

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Santosh Kumar. 2015-07-31. Gap probabilities and densities of extreme eigenvalues of random matrices: Exact results. https://arxiv.org/abs/1507.08830

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