Título: The environment seen from a geodesic in last-passage percolation, and the TASEP seen from a second-class particle.

Palestrante: James Martin
Data: 28/04/2021
Horario: 13:00h
Local: Transmissão online.

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ID da reunião: 958 0581 3232

Resumo: We study directed last-passage percolation in Z^2 with i.i.d. exponential weights. What does a geodesic path look like locally, and how do the weights on and nearby the geodesic behave? We show convergence of the distribution of the "environment" as seen from a typical point along the geodesic in a given direction, as its length goes to infinity. We describe the limiting distribution, and can calculate various quantities such as the density function of a typical weight, or the proportion of "corners" along the path. The analysis involves a link with the TASEP (totally asymmetric simple exclusion process) seen from an isolated second-class particle, and we obtain some new convergence and ergodicity results for that process. The talk is based on joint work with Allan Sly and Lingfu Zhang