Population dynamics simulations of large deviations for three subclasses of the Kardar-Parisi-Zhang universality class

TL;DR

This paper introduces a population dynamics simulation method to study large deviations in the KPZ universality class, confirming some theoretical predictions and revealing new insights into initial condition effects.

Contribution

It develops a versatile numerical approach for analyzing large deviations in the KPZ class, including cases previously unexplored.

Findings

Confirmed theoretical predictions for step initial conditions

Characterized large deviations for flat and stationary initial conditions

Discovered robustness of negative large deviations across initial conditions

Abstract

Recent theoretical studies have gradually deepened our understanding of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class even in the large deviation regime, but numerical methods for studying KPZ large deviations remain limited. Here we implement a method based on the population dynamics algorithm for studying large deviations of time-integrated local currents in the totally asymmetric simple exclusion process (TASEP), which is a pragmatic model in the 1D KPZ class. Carrying out simulations for the three representative initial conditions, namely step, flat, and stationary ones, we not only confirm theoretical predictions available for the step case, but also characterize large deviations for the flat and stationary cases which have not been investigated before. We reveal in particular an unexpected robustness of the deeply negative large deviation regime with respect to different initial conditions. We attribute this robustness to the spontaneous formation of a wedge shape in interface profile. Our population dynamics approach may serve as a versatile method for studying large deviations in the KPZ class numerically and, potentially, even experimentally.