Author

Ruizhe Zhang

Simons Institute for the Theory of Computing

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Preprint Aug 2026

Hit-and-Run Mixes as Fast as the Ball Walk

Let $K\subset\mathbb{R}^n$ be an isotropic convex body. We prove that the hit-and-run walk, started from any $M$-warm distribution, reaches total-variation distance $\varepsilon$ from the uniform distribution on $K$ in $O\!\left(n^2\psi_n^{-2}\log^3(M/\varepsilon)\right)$ steps, where $\psi_n^{-1}$ is the Kannan-Lov\'a...

Ruizhe Zhang · 0 citations