A Note on the Polynomial Ergodicity of the One-Dimensional Zig-Zag process

TL;DR

This paper establishes polynomial ergodicity for the one-dimensional Zig-Zag process on heavy-tailed distributions, specifically identifying the precise polynomial rate of convergence for Student distributions.

Contribution

It provides the first rigorous proof of polynomial ergodicity for the Zig-Zag process on heavy-tailed targets and determines the exact convergence order for Student distributions.

Findings

Proves polynomial ergodicity for heavy-tailed targets.

Identifies the exact polynomial convergence rate for Student distributions.

Enhances understanding of Zig-Zag process behavior on complex distributions.

Abstract

We prove polynomial ergodicity for the one-dimensional Zig-Zag process on heavy tailed targets and identify the exact order of polynomial convergence of the process when targeting Student distributions.