Event-chain Monte Carlo: foundations, applications, and prospects

TL;DR

This review paper explores the foundations, applications, and future prospects of event-chain Monte Carlo (ECMC), a non-reversible Markov chain method, highlighting its theoretical basis, model applications, and potential in molecular simulation.

Contribution

It provides a comprehensive overview of ECMC's mathematical foundations, analyzes its performance in statistical physics models, and discusses its application to complex molecular systems.

Findings

ECMC offers efficient sampling in statistical physics models

The method shows promise for molecular simulation of peptides and proteins

ECMC's performance surpasses traditional Markov chain methods in certain applications

Abstract

This review treats the mathematical and algorithmic foundations of non-reversible Markov chains in the context of event-chain Monte Carlo (ECMC), a continuous-time lifted Markov chain that employs the factorized Metropolis algorithm. It analyzes a number of model applications, and then reviews the formulation as well as the performance of ECMC in key models in statistical physics. Finally, the review reports on an ongoing initiative to apply the method to the sampling problem in molecular simulation, that is, to real-world models of peptides, proteins, and polymers in aqueous solution.