# Kinetic walks for sampling

## TL;DR

This paper introduces and analyzes discrete-time kinetic walk algorithms, including a Zig-Zag sampler and hybrid jump/diffusion methods, for efficient sampling of complex distributions, extending continuous kinetic models to discrete settings.

## Contribution

It defines and studies a discrete-space Zig-Zag sampler and hybrid kinetic samplers, bridging continuous models and discrete algorithms for sampling in high-dimensional spaces.

## Key findings

- Discrete Zig-Zag sampler effectively samples from target distributions.
- Hybrid jump/diffusion samplers handle multi-scale potentials efficiently.
- The methods extend continuous kinetic processes to discrete frameworks.

## Abstract

The persistent walk is a classical model in kinetic theory, which has also been studied as a toy model for MCMC questions. Its continuous limit, the telegraph process, has recently been extended to various velocity jump processes (Bouncy Particle Sampler, Zig-Zag process, etc.) in order to sample general target distributions on $\mathbb R^d$. This paper studies, from a sampling point of view, general kinetic walks that are natural discrete-time (and possibly discrete-space) counterparts of these continuous-space processes. The main contributions of the paper are the definition and study of a discrete-space Zig-Zag sampler and the definition and time-discretisation of hybrid jump/diffusion kinetic samplers for multi-scale potentials on $\mathbb R^d$.