Vető Bálint (BME): Directed polymer models and the Kardar--Parisi--Zhang equation

The Kardar--Parisi--Zhang (KPZ) equation provides a description of random surface growth in physics, e.g. crystallization, burning front evolution, coffee ring. The solution can be represented as the free energy of the continuum directed random polymer via a Feynman-Kac type formula. First in this talk, an overview is given on the KPZ equation and universality class, directed polymer models. Then results on the stationary KPZ equation are presented based on the directed polymer approach. Further, some recent limit theorems on directed polymers are explained. Based on joint work with A. Borodin, I. Corwin, P. Ferrari and Zs. Talyigás.