Geometry of geodesics in integrable models of planar last passage percolation

par Riddhipratim Basu (ICTS Tata Institute of Fundamental Research )

jeudi 19 nov. 2020, 14:00 → 15:00 Europe/Paris

A préciser

 In planar first and last passage percolation, one considers an i.i.d. field of noise and the weight of a given path is obtained by integrating the noise along it. The object of interest then is the optimum weight of a path joining two given far away vertices and the geodesic that attains it. Under rather general conditions, these models are believed to be in the Kardar-Parisi-Zhang (KPZ) universality class and are conjectured to exhibit  a number of shared universal features governing the weight and geometry of the geodesics. The rigorous understanding of this, however, is mostly limited to the integrable, or, exactly solvable, models of last passage percolation. In this talk, we shall discuss some recent and some not so recent results regarding the geometry of geodesics in certain exactly solvable models of planar last passage percolation focussing on transversal fluctuations, coalescence and rarity of disjoint geodesics among others.