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Alessandra Occelli: Time covariance for last passage percolation in half-space

Time: Tue 2022-04-26 15.15 - 16.15

Location: Zoom, meeting ID: 698 3346 0369

Participating: Alessandra Occelli (UMPA ENS Lyon)

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We consider a last passage percolation model in half space with exponential weights. We show that,when the two are at small macroscopic distance, then the first order correction to the two-time 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. Based on joint work with Patrik Ferrari.