On Hamiltonian Monte Carlo for Gaussian Random Variables with Random Hamiltonians
Probability
2026-03-02 v1 Dynamical Systems
Abstract
We study a family of (multivariate-)Gaussian Hamiltonian Monte Carlo (GHMC) operators and prove that the family of Gaussian distributions and their mixtures are invariant under such operators. Furthermore, each such operator is a contraction on the space of parameters and an explicit formulae are derived. These results then enable us to analyze the dynamics and convergences of independent and identically distributed random sequences of such operators.
Cite
@article{arxiv.2602.24256,
title = {On Hamiltonian Monte Carlo for Gaussian Random Variables with Random Hamiltonians},
author = {Yingdong Lu and Tomasz Nowicki},
journal= {arXiv preprint arXiv:2602.24256},
year = {2026}
}