Fractal geometry in models of random growth
19th May 2021, 4:00 pm – 5:00 pm
In last passage percolation models predicted to lie in the Kardar-Parisi-Zhang (KPZ) universality class, geodesics are oriented paths moving through random noise accruing maximum weight. The weight of such geodesics as their endpoints are varied gives rise to an intricate random energy field expected to converge to a rich universal object known as the Directed Landscape constructed by Dauvergne, Ortmann and Virag.
Reporting recent progress in our understanding of the random fractal geometry exhibited by the latter, we will discuss results about the coupling structure of the geodesic weight as the endpoints are varied.
The talk will be based on joint works with subsets of R. Basu, E. Bates, A. Hammond and M. Hegde.