We present a polynomial-time randomized algorithm for estimating the permanent of an arbitrary $M \times M$ real matrix $A$ up to an additive error. We do this by viewing the permanent of $A$ as the expectation of a product of a centered joint Gaussian random variables whose covariance matrix we call the Gaussian embedding of $A$. The algorithm outputs the empirical mean $S_{N}$ of this product after sampling from this multivariate distribution $N$ times. In particular, after sampling $N$ samples, our algorithm runs in time $O(MN)$ with failure probability \begin{equation*} P(|S_{N}-\text{perm}(A)| > t) \leq \frac{3^{M}}{t^{2}N}\alpha^{2M} \end{equation*} for $\alpha \geq \|A \|$.

翻译：我们提出一个多元时间随机算法,用于估计任意的M美元/乘以M美元实际基质$A的永久值,直至一个添加错误。我们这样做的方法是,将永久值A美元视为一个中央联合高斯随机变量的产物的预期值,我们称其共变数矩阵为高斯嵌入$A。在从这一多变分布中取样后算出该产品的实证平均值$S%N美元乘以该多变数分配的倍数。特别是,在抽样取样后,我们的算法在时间上以美元(MN)为单位运行,失败概率为$(O)$P(S)/N}-\ t{text{perm}(A)>\leq\frac{3 ⁇ M ⁇ 2}N ⁇ alpha2M}\end{quation ⁇ $\quation $ALpha\geq_A ⁇ $。