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arXiv · 1807.02982

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

Patrik L. Ferrari·Alessandra Occelli
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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.

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Patrik L. Ferrari, Alessandra Occelli. 2018-07-09. Time-time covariance for last passage percolation with generic initial profile. https://doi.org/10.1007/s11040-018-9300-6

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