BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lingfu Zhang (Princeton) DTSTART:20211029T163000Z DTEND:20211029T173000Z DTSTAMP:20260423T005651Z UID:PatC/47 DESCRIPTION:Title: Th e environment seen from a geodesic in last-passage percolation\nby Lin gfu Zhang (Princeton) as part of Probability and the City Seminar\n\n\nAbs tract\nIn exponential directed last-passage percolation\, each vertex in Z ^2 is assigned an i.i.d. exponential weight\, and the geodesic between a p air of vertices refers to the up-right path connecting them\, with the max imum total weight along the path. It is a natural question to ask what a g eodesic looks like locally\, and how weights on and nearby the geodesic be have. In this talk\, I will present some new results on this. We show conv ergence of the distribution of the ‘environment’ as seen from a typica l point along the geodesic\, and convergence of the corresponding empirica l measure\, as the geodesic length goes to infinity. In addition\, we obta in an explicit description of the limiting environment\, which depends on the direction of the geodesic. This in principle enables one to compute al l the local statistics of the geodesic\, and I will talk about some surpri sing and interesting examples. This is based on joint work with James Mart in and Allan Sly.\n LOCATION:https://researchseminars.org/talk/PatC/47/ END:VEVENT END:VCALENDAR