Time-time covariance for last passage percolation in half-space. (English) Zbl 07829152

Ferrari, Patrik; Occelli, Alessandra

Ann. Appl. Probab. 34, No. 1A, 627-674 (2024).

Summary: This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first-order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-point process as well as localization of the geodesics. Unlike for the full-space case, for half-space we have to overcome the difficulty that the point-to-point model in half-space with generic start and end-points is not known.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
82C22	Interacting particle systems in time-dependent statistical mechanics
82B43	Percolation

Keywords:

last passage percolation; KPZ universality class; time-time correlations; half-space models

References:

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