Polynuclear Growth and the Toda Lattice

Explore the intricacies of polynuclear growth and its connection to the Toda lattice in this 51-minute lecture by Jeremy Quastel, presented at the Workshop on box-ball systems from integrable systems and probabilistic perspectives. Delve into the polynuclear growth model, a crucial component of the KPZ universality class, and its study beyond the traditional droplet geometry. Discover how this model relates to the longest increasing subsequence of random permutations and learn about its properties as an integrable Markov process. Examine the key structures shared with the KPZ fixed point, including determinantal formulas for transition probabilities and fixed-time n-point distributions governed by the non-Abelian 2D Toda lattice. Gain insights into this collaborative research with Konstantin Matetski and Daniel Remenik, presented at the Centre de recherches mathématiques (CRM) as part of a specialized workshop on mathematical systems.