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

We study aging properties for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution of 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. 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. The key ingredient to our proofs is a covariance-to-variance reduction which is a characteristic of space-time stationarity and allows to deduce the asymptotic behavior of the correlations of two points by the one of the variance at one point. We formulate several open problems.