Author

Santosh S. Vempala

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Preprint Aug 2026

Spectral Gaps of Hit-and-Run and Coordinate Hit-and-Run

For any convex body $\mathcal{K}\subset\mathbb{R}^{n}$ containing a unit ball, the spectral gap of Hit-and-Run is $\Omega(1/(n^2 C_{\mathsf{PI}}))$, where $C_{\mathsf{PI}}$ is the Poincar\'e constant of the uniform distribution $\pi$ over $\mathcal{K}$. This implies that Hit-and-Run converges to a distribution within $...

Yunbum Kook, Santosh S. Vempala · 2 citations