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T-R McLaughlin, Tamara Grava, Tom Claeys","submitted_at":"2014-10-26T08:41:21Z","abstract_excerpt":"We obtain large N asymptotics for the Hermitian random matrix partition function \\[Z_N(V)=\\int_{\\mathbb R^N}\\prod_{i<j}(x_i-x_j)^2 \\prod_{j=1}^N e^{-N V(x_j)}dx_j,\\] in the case where the external potential $V$ is a polynomials such that the random matrix eigenvalues accumulate on two disjoint intervals (the two-cut case). We compute leading and sub-leading terms in the asymptotic expansion for $\\log Z_N(V)$, up to terms that are small as $N$ goes to infinity. 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T-R McLaughlin, Tamara Grava, Tom Claeys","submitted_at":"2014-10-26T08:41:21Z","abstract_excerpt":"We obtain large N asymptotics for the Hermitian random matrix partition function \\[Z_N(V)=\\int_{\\mathbb R^N}\\prod_{i<j}(x_i-x_j)^2 \\prod_{j=1}^N e^{-N V(x_j)}dx_j,\\] in the case where the external potential $V$ is a polynomials such that the random matrix eigenvalues accumulate on two disjoint intervals (the two-cut case). We compute leading and sub-leading terms in the asymptotic expansion for $\\log Z_N(V)$, up to terms that are small as $N$ goes to infinity. 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