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Polytope Sampling at the Speed of Isoperimetry
We give faster algorithms for sampling from the uniform distribution over a polytope. Our main result is an algorithm that, when applied to a polytope with $m$ constraints in $n$ dimensions, uses $m \cdot \mathrm{poly}\log(\frac m δ)$ iterations, each running in time $O(mn^{ω- 1})$, to return a samp
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