Non-reversible Monte Carlo: an example of 'true' self-repelling motion

TL;DR

This paper establishes a connection between non-reversible Monte Carlo algorithms, lifted TASEP, and self-repelling motion, demonstrating that empirical distributions from Monte Carlo match analytic solutions of the self-repelling model.

Contribution

It introduces a novel link between non-reversible Monte Carlo methods and an exactly solvable self-repelling motion model, providing new analytical insights.

Findings

Monte Carlo empirical distributions align with self-repelling motion solutions

Demonstrates the analytical solvability of the self-repelling model

Links between Monte Carlo dynamics and self-repelling processes established

Abstract

We link the large-scale dynamics of non-reversible Monte Carlo algorithms as well as a lifted TASEP to an exactly soluble model of self-repelling motion. We present arguments for the connection between the problems and perform simulations, where we show that the empirical distribution functions generated from Monte Carlo are well described by the analytic solution of self-repelling motion.