# Complexity of zigzag sampling algorithm for strongly log-concave distributions

arXiv: https://arxiv.org/abs/2012.11094 · HTML: https://mlsanity.com/paper/2012.11094/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2020.

## Built on by (most cited first, 5 of 5)

- [Faster high-accuracy log-concave sampling via algorithmic warm starts](https://mlsanity.com/paper/2302.10249/) (2023)
- [High-accuracy sampling for diffusion models and log-concave distributions](https://mlsanity.com/paper/2602.01338/) (2026)
- [Mean-Square Analysis of Discretized Ito Diffusions for Heavy-tailed Sampling](https://mlsanity.com/paper/2303.00570/) (2023)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [Windowed thinning and query complexity for the bouncy particle and Zigzag samplers](https://mlsanity.com/paper/2607.28413/) (2026)

## Abstract (arXiv)

We study the computational complexity of zigzag sampling algorithm for strongly log-concave distributions. The zigzag process has the advantage of not requiring time discretization for implementation, and that each proposed bouncing event requires only one evaluation of partial derivative of the potential, while its convergence rate is dimension independent. Using these properties, we prove that the zigzag sampling algorithm achieves varepsilon error in chi-square divergence with a computational cost equivalent to Obigl(kappa2 d^frac12(logfrac1varepsilon)^frac32bigr) gradient evaluations in the regime kappa ll fracdlog d under a warm start assumption, where kappa is the condition number and d is the dimension.