# An optimal $(\epsilon,\delta)$-approximation scheme for the mean of random variables with bounded relative variance

@article{Huber2017AnO, title={An optimal \$(\epsilon,\delta)\$-approximation scheme for the mean of random variables with bounded relative variance}, author={Mark L. Huber}, journal={arXiv: Computation}, year={2017} }

Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random variables $X_1,X_2,\ldots$ with finite mean $\mu$ and standard deviation$\sigma$ such that $\mu$ is the solution for the problem input, and the relative standard deviation $|\sigma/\mu| \leq c$ for known $c$. Under these circumstances, it is known that the number of…

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