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Subject: directed polymers in random environment ×

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    Aging for the stationary Kardar--Parisi--Zhang equation and related models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Deuschel, Jean-Dominique; Orenshtein, Tal; Moreno Flores, Gregorio R.
    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.