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Aging for the stationary Kardar-Parisi-Zhang equation and related models
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.Comment: 34 pages. In the second version the introduction as well as the list
of references were extende
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Aging for the stationary Kardar--Parisi--Zhang equation and related models
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
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