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Time-time Covariance for Last Passage Percolation with Generic Initial Profile

  • P. L. FerrariEmail author
  • A. Occelli
Article
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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 Ferrari and Spohn (2011). 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.

Keywords

Last passage percolation KPZ universality class Time-time correlations 

Mathematics Subject Classification (2010)

60K35 82C22 82B43 

Notes

Acknowledgments

This work is supported by the German Research Foundation in the Collaborative Research Center 1060 “The Mathematics of Emergent Effects”, project B04.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute for Applied MathematicsBonn UniversityBonnGermany

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