Time-time covariance for last passage percolation with generic initial profile

Understand

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.