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A remark on approximating permanents of positive definite matrices (2005.06344v1)
Published 13 May 2020 in cs.DS and math.CO
Abstract: Let $A$ be an $n \times n$ positive definite Hermitian matrix with all eigenvalues between 1 and 2. We represent the permanent of $A$ as the integral of some explicit log-concave function on ${\Bbb R}{2n}$. Consequently, there is a fully polynomial randomized approximation scheme (FPRAS) for the permanent of $A$.
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