Special sessions

A four day short course (19, 20, 22 and 23/1/2026 10:30-12:00 at P3.10@Técnico and online) by

Daniel Remenik, Center for Mathematical Modeling, Universidad de Chile
An introduction to the KPZ universality class

The one-dimensional Kardar-Parisi-Zhang (KPZ) universality class is a broad collection of models including one-dimensional random interface growth, directed polymers and particle systems. At its center lies the KPZ fixed point, a scaling invariant Markov process which governs the asymptotic fluctuations of all models in the class, and which contains all the rich fluctuation behavior seen in the class.

In these lectures, I will explain how one can derive explicit formulas for the transition probabilities of the KPZ fixed point, and how they reveal connections with random matrix theory and with certain classical integrable differential equations. As a starting point for the derivation, we will use the polynuclear growth model (PNG), a model for crystal growth in one dimension that is intimately connected to the classical longest increasing subsequence problem for a uniformly chosen random permutation. The solution will be obtained through a mix of probabilistic and integrable methods.

The lectures will begin with a general overview of the KPZ universality class and its conjectural scaling limits, and I will aim to keep prerequisite knowledge to a minimum.

Permanent link to this information: https://pmp.math.tecnico.ulisboa.pt/lecture_series?sgid=110