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Random growth in 1+1 dimensions, KPZ and KP

Daniel Remenik, Universidad de Chile
Monday, May 10, 2021 - 2:30pm to 3:20pm

The KPZ fixed point is the Markov process which arises as the universal scaling limit of all models in the KPZ universality class, a broad collection of models including one-dimensional random growth, directed polymers and particle systems. In particular, it contains all of the rich fluctuation behavior seen in the class, which for some initial data relates to distributions from random matrix theory (RMT). In this talk I'm going to introduce this process and explain how its finite-dimensional distributions are connected to a famous integrable dispersive PDE, the Kadomtsev-Petviashvili (KP) equation (and, for some special initial data, the simpler Korteweg-de Vries equation). I will also describe how this relation provides an explanation for the appearance in the KPZ universality class of the Tracy-Widom distributions from RMT.

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