Speaker: Riddhipratim Basu, ICTS
January 1, 2024 02:30 PM
- 03:30 PM
Abstract:
First passage percolation (FPP), usually studied on the nearest neighbour graph of Zd, puts independent and identically distributed random positive weights on the edges of the graph and considers the minimum weight among all paths joining two vertices. This can be interpreted either as a model for fluid flow through inhomogeneous media or as a random distortion of the graph distance. Introduced almost 60 years ago, FPP remains one of the most challenging models in spatial probability. In dimension 2, precise predictions are available from the theory of Kardar-Parisi-Zhang (KPZ) universality class which is believed to contain planar FPP models under mild conditions on the noise field, but sharp results have mostly remained out of reach. I shall describe some of the major open problems and discuss a bit of what is known, including some recent results with Vladas Sidoravicius and Allan Sly for variants of planar FPP models that enjoy rotational symmetry.