Aging for the stationary Kardar-Parisi-Zhang equation and related models

TL;DR

This paper investigates aging phenomena in stationary models within the KPZ universality class, demonstrating universal aging behavior and contrasting it with the Edwards-Wilkinson class, using covariance-to-variance reduction techniques.

Contribution

It establishes the presence of aging in various KPZ models and introduces covariance-to-variance reduction as a key analytical tool.

Findings

Aging observed in stationary KPZ fixed point and related models.

Universal decay behavior characterized by correlation decay rates.

Different decay exponents identified for KPZ and Edwards-Wilkinson classes.

Abstract

We study the aging property for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary KPZ equation, the height function of the stationary TASEP, last-passage percolation with boundary conditions and stationary directed polymers in the intermediate disorder regime. All of these models are shown to display a universal aging behavior characterized by the rate of decay of their correlations. As a comparison, we show aging for models in the Edwards-Wilkinson universality class where a different decay exponent is obtained. A key ingredient to our proofs is a characteristic of space-time stationarity - covariance-to-variance reduction - which allows to deduce the asymptotic behavior of the correlations of two space-time points by the one of the variances at one point. We formulate several open problems.