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

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.

arXiv comment33 pages; minor corrections

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Cited by in corpus (12)

• The directed landscape
• Stationary half-space last passage percolation
• Partial yet definite emergence of the Kardar-Parisi-Zhang class in isotropic spin chains
• Temporal Correlation in Last Passage Percolation with Flat Initial Condition via Brownian Comparison
• Half-space stationary Kardar-Parisi-Zhang equation beyond the Brownian case
• Optimal-order exit point bounds in exponential last-passage percolation via the coupling technique
• The Long ans Short Time Asymptotics of the Two-Time Distribution in Local Random Growth
• Moderate deviation and exit time estimates for stationary Last Passage Percolation
• KPZ fluctuations in finite volume
• On the exponent governing the correlation decay of the Airy${}_1$ process
• Coupling derivation of optimal-order central moment bounds in exponential last-passage percolation
• The half-space Airy stat process