# Rapid Mixing of Hamiltonian Monte Carlo on Strongly Log-Concave Distributions

arXiv: https://arxiv.org/abs/1708.07114 · HTML: https://mlsanity.com/paper/1708.07114/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2017.

## Built on by (most cited first, 12 of 12)

- [Mixing Time Guarantees for Unadjusted Hamiltonian Monte Carlo](https://mlsanity.com/paper/2105.00887/) (2021)
- [When does Metropolized Hamiltonian Monte Carlo provably outperform Metropolis-adjusted Langevin algorithm?](https://mlsanity.com/paper/2304.04724/) (2023)
- [When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpoint](https://mlsanity.com/paper/2110.01827/) (2021)
- [Asymptotic bias of inexact Markov Chain Monte Carlo methods in high dimension](https://mlsanity.com/paper/2108.00682/) (2021)
- [Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo](https://mlsanity.com/paper/2401.11665/) (2024)
- [An Introduction to Hamiltonian Monte Carlo Method for Sampling](https://mlsanity.com/paper/2108.12107/) (2021)
- [Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport](https://mlsanity.com/paper/2202.01841/) (2022)
- [Entropy-based adaptive Hamiltonian Monte Carlo](https://mlsanity.com/paper/2110.14625/) (2021)
- [Faster Sampling via Stochastic Gradient Proximal Sampler](https://mlsanity.com/paper/2405.16734/) (2024)
- [Ensemble-Based Annealed Importance Sampling](https://mlsanity.com/paper/2401.15645/) (2024)
- [Hamiltonian Adaptive Importance Sampling](https://mlsanity.com/paper/2209.13716/) (2022)
- [Hamiltonian Monte Carlo with Asymmetrical Momentum Distributions](https://mlsanity.com/paper/2110.12907/) (2021)

## Abstract (arXiv)

We obtain several quantitative bounds on the mixing properties of the Hamiltonian Monte Carlo (HMC) algorithm for a strongly log-concave target distribution π on ℝd, showing that HMC mixes quickly in this setting. One of our main results is a dimension-free bound on the mixing of an "ideal" HMC chain, which is used to show that the usual leapfrog implementation of HMC can sample from π using only O(d^frac14) gradient evaluations. This dependence on dimension is sharp, and our results significantly extend and improve previous quantitative bounds on the mixing of HMC.