Random interfaces, geodesics and the directed landscape
A talk in the Summer School Randomness in Physics & Mathematics series by Bálint Virág
Coastlines, the edge of burned paper, the boundary of coee spots,
the game of Tetris: random interfaces surround us. Still, the mathematical theory
of one of the the most important cases, the "KPZ universality class", has only been
cracked very recently.
This class is related to trac models, longest increasing subsequences of random
permutations, the RSK correspondence, last passage percolation, integrable probability
systems and the stochastic heat equation. A new random metric in the plane,
the "directed landscape" captures the essence of these problems.