KPZ equation correlations in time

We consider the narrow wedge solution to Kardar–Parisi–Zhang stochastic PDE under characteristic 3:2:1 scaling of time, space and fluctuations. study correlation fluctuations at two different times. show that, when times are close each other, approaches one a power-law rate with exponent 2/3, while, remote from tends zero ?1/3. also prove exponential-type tail bounds for differences space-time points. Three main tools pivotal proving these results: (1) representation two-time distribution in terms independent solutions, (2) Brownian Gibbs property KPZ line ensemble (3) recently proved one-point on solution.