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Time covariance (and stationarity) for last passage percolation models

Date: Thursday, March 7, 2019 16:00 - 17:00
Speaker: Alessandra Occelli (Uni Bonn)
Location: Big Seminar room Ground floor / Office Bldg West (I21.EG.101)
Series: Mathematics and CS Seminar
Host: Laszlo Erdös
Contact: PETZ Caroline
Lab building west seminar room

We study time correlations of last passage percolation (LPP), a model in the Kardar-Parisi-Zhang universality class, with different geometries: step, flat, stationary and general random. We prove the convergence of the covariances of the LPP at two different times to a limiting expression given in terms of Airy processes.
Furthermore, we prove the behaviour of the covariances when the two times are close to each other, conjectured in a work of Ferrari and Spohn.
If time permits, we will present a stationary version of the LPP with half-space geometry and see how the previous results could be extended to this model.
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