# A mixing time bound for Gibbs sampling from log-smooth log-concave distributions

arXiv: https://arxiv.org/abs/2412.17899 · HTML: https://mlsanity.com/paper/2412.17899/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 28 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [Entropy contraction of the Gibbs sampler under log-concavity](https://mlsanity.com/paper/2410.00858/) (2024)
- [On the ℓ0 Isoperimetric Coefficient of Measurable Sets](https://mlsanity.com/paper/2312.00015/) (2023)

## Built on by (most cited first, 2 of 2)

- [Local and Mixing-Based Algorithms for Gaussian Graphical Model Selection from Glauber Dynamics](https://mlsanity.com/paper/2412.18594/) (2024)
- [Mixing-Free and Signal-Optimal Learning of Gaussian Graphical Models from Glauber Dynamics](https://mlsanity.com/paper/2607.18559/) (2026)

## Abstract (arXiv)

The Gibbs sampler, also known as the coordinate hit-and-run algorithm, is a Markov chain that is widely used to draw samples from probability distributions in arbitrary dimensions. At each iteration of the algorithm, a randomly selected coordinate is resampled from the distribution that results from conditioning on all the other coordinates. We study the behavior of the Gibbs sampler on the class of log-smooth and strongly log-concave target distributions supported on ℝn. Assuming the initial distribution is M-warm with respect to the target, we show that the Gibbs sampler requires at most Ostarleft(kappa2 n7.5left(maxleft1,√frac1nlog frac2Mγrightright)2right) steps to produce a sample with error no more than γ in total variation distance from a distribution with condition number kappa.