Séminaire de Probabilités commun ICJ/UMPA

Polynuclear growth and the Toda lattice

by Mr Jeremy Quastel (University of Toronto)

Fokko du Cloux (ICJ, Bâtiment Braconnier)

The polynuclear growth model is one of the most important models in the KPZ universality class. Generally it has been studied in the droplet geometry, where it is equivalent to the longest increasing subsequence of a random permutation, whose solution sparked the KPZ revolution. We study it for general initial data and show that it is an integrable Markov process sharing the key structures of the KPZ fixed point, determinantal formulas for the transition probabilities and fixed time n-point distributions governed by completely integrable equations, the non-Abelian 2D Toda lattice. Joint with Konstantin Matetski and Daniel Remenik.