Polynuclear Growth models: Old and new results

10.04.2025, 12:15  –  Campus Golm, Building 09, Room 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Alessandra Occelli (Angers)

In this talk I will discuss polynuclear growth model with different symmetries and boundary conditions. I will highlight their connections to problems in combinatorics (Ulam's problem), in analysis (Painlevé II equation), in mathematical physics (KPZ growth models) and in random matrix theory. I will sketch the strategy to study the model in the half space setting with two external sources, strategy which relies on algebraic and orthogonal polynomials identities, and Riemann--Hilbert techniques, and which led to a limit distribution formulated in terms of the solution to Painlevé II equation. This result proves a conjecture by Barraquand--Krajenbrink--Le Doussal '22 on the distribution of the stationary KPZ equation on the half line. Based on joint work with M. Cafasso, D. Ofner, H. Walsh.