# Convergence of Preconditioned Hamiltonian Monte Carlo on Hilbert Spaces

arXiv: https://arxiv.org/abs/2011.08578 · HTML: https://mlsanity.com/paper/2011.08578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2020.

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

- [Infinite-Dimensional Diffusion Models](https://mlsanity.com/paper/2302.10130/) (2023)
- [Feel-Good Thompson Sampling for Contextual Bandits: a Markov Chain Monte Carlo Showdown](https://mlsanity.com/paper/2507.15290/) (2025)

## Abstract (arXiv)

In this article, we consider the preconditioned Hamiltonian Monte Carlo (pHMC) algorithm defined directly on an infinite-dimensional Hilbert space. In this context, and under a condition reminiscent of strong log-concavity of the target measure, we prove convergence bounds for adjusted pHMC in the standard 1-Wasserstein distance. The arguments rely on a synchronous coupling of two copies of pHMC, which is controlled by adapting elements from arXiv:1805.00452.