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Let $A$ be an $n \times n$ positive definite Hermitian matrix with alleigenvalues between 1 and 2. We represent the permanent of $A$ as the integralof some explicit log-concave function on ${\Bbb R}^{2n}$. Consequently, thereis a fully polynomial randomized approximation scheme (FPRAS) for the permanentof $A$.

A remark on approximating permanents of positive definite matrices