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The smallest eigenvalue distribution at the spectrum edge of random matrices
Institution:1. Department of Physics, Graduate School of Science, Osaka University, Toyonaka, Osaka 500, Japan;2. Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia;1. Departamento de Física and Centro Científico-Tecnológico de Valparaíso-CCTVal, Universidad Técnica Federico Santa María, Valparaíso, Chile;2. Physics Department, State University of Tetovo, Ilinden Street nn, 1200, Tetovo, Macedonia;3. Center for Astro, Particle and Planetary Physics, New York University Abu Dhabi, Abu Dhabi, United Arab Emirates;4. Frankfurt Institute for Advanced Studies (FIAS), Frankfurt am Main, Germany;5. Institut für Theoretische Physik, Goethe-Universität, Frankfurt am Main, Germany;1. Department of Mathematics, Stanford University, United States of America;2. Department of Statistics, Stanford University, United States of America;1. Department of Mathematics, University of California, Berkeley, CA 94720, USA;2. Departamento de Matemática Aplicada & IUMA, Universidad de Zaragoza, María de Luna 3, 50018 Zaragoza, Spain;1. National Mobile Communications Research Lab, Southeast University, Nanjing, 210096, China;2. State Key Lab. of Millimeter Waves, Southeast University, Nanjing, 210096, China
Abstract:Pfaffian expressions are derived for the smallest eigenvalue distributions of Laguerre orthogonal and symplectic ensembles of random matrices. Asymptotic forms of the smallest eigenvalue distributions are evaluated in the limit of large matrix dimension.
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