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

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.