# Ergodicity of Markov chain Monte Carlo with reversible proposal

arXiv: https://arxiv.org/abs/1602.02889 · HTML: https://mlsanity.com/paper/1602.02889/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2016.

## Built on by (most cited first, 1 of 1)

- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)

## Abstract (arXiv)

We describe ergodic properties of some Metropolis-Hastings (MH) algorithms for heavy-tailed target distributions. The analysis usually falls into sub-geometric ergodicity framework but we prove that the mixed preconditioned Crank-Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that the MpCN algorithm becomes a random-walk Metropolis algorithm under suitable transformation.