# Shaken dynamics: an easy way to parallel Markov Chain Monte Carlo

## TL;DR

This paper introduces a class of reversible parallel Markov Chain Monte Carlo dynamics for spin systems, providing explicit stationary measures and applications to parallel algorithms in combinatorial optimization.

## Contribution

It defines a new class of parallel MCMC dynamics for spin systems, with explicit stationary measures and convergence properties, suitable for parallel algorithms.

## Key findings

- Dynamics are reversible with explicit stationary measures.
- Convergence to equilibrium is analyzed on a62.
- Applications to parallel algorithms for combinatorial optimization.

## Abstract

We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function $H(\sigma)$. These dynamics turn out to be reversible and their stationary measure is explicitly determined. Convergence to equilibrium and relation of the stationary measure to the usual Gibbs measure are discussed when the dynamics is defined on $\mathbb{Z}^2$. Further it is shown how these dynamics can be used to define natively parallel algorithms to face problems in the context of combinatorial optimization.