# Patrik Ferrari: Time-time covariance for last passage percolation with generic initial profile

**Time: **
Tue 2019-10-15 15.15 - 16.15

**Lecturer: **
Patrik Ferrari

**Location: ** F11, KTH

### Abstract

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 [SIGMA 12 (2016), 074]. 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.