Time-time covariance for last passage percolation with generic initial profile. (English) Zbl 1405.60144
Summary: We consider time correlation for KPZ growth in \(1+1\) dimensions in a neighborhood of a characteristics. We prove convergence of the covariance with droplet, flat and stationary initial profile. In particular, this provides a rigorous proof of the exact formula of the covariance for the stationary case obtained in [P. L. Ferrari and H. Spohn, in: The Oxford handbook of random matrix theory. Oxford: Oxford University Press. 782–801 (2011; Zbl 1234.60010)]. Furthermore, we prove the universality of the first order correction when the two observation times are close and provide a rigorous bound of the error term. This result holds also for random initial profiles which are not necessarily stationary.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82B43 | Percolation |
Citations:
Zbl 1234.60010References:
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