A remark on approximating permanents of positive definite matrices

05/13/2020

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by   Alexander Barvinok, et al.

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Let A be an n × 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 R^2n. Consequently, there is a fully polynomial randomized approximation scheme (FPRAS) for the permanent of A.