KPZ Universality and Directed Polymers
​Universalité de Kardar-Parisi-Zhang et polymères dirigés
January-June 2017

The theory of directed polymers and Kardar-Parisi-Zhang (KPZ) scalings is one the most active areas in statistical mechanics and mathematical physics in the last 10 years. Directed polymers are random walks in a disordered environment given by a random potential. For a fixed realization of a potential, one either consider a probability distribution on paths of a given length n, so-called polymer measure, or a single action-minimizing path corresponding to a limit of zero temperature. The main problem is to understand the asymptotic behaviour of both objects in the limit of large n. A big progress has been achieved very recently in deriving exact formulas related to Tracy-Widom distributions and Airy processes. It was shown by exact calculations that many models belong to the KPZ universality class. However it is expected that universality holds for extremely general class of disordered systems in dimension 1+1. It is a rare case when highly non-trivial scaling behaviour conjecturally describes both zero temperature (like geodesics in random metric, or action minimizing paths) and positive temperature regimes. It is important to emphasize that the problem is essentially interdisciplinary. It involves ideas from statistical mechanics, probability, dynamics, and PDEs.
> Prof. Konstantin KHANIN
University of Toronto
Local Project Leader
Prof. Senya SHLOSMAN
CNRS, Centre de physique théorique
Aix-Marseille Université

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Random Structures in Statistical Mechanics and Mathematical Physics (1559)
Structures aléatoires en mécanique statistique et physique mathématique

6-10 March 2017
Qualitative Methods in KPZ Universality (1558)
Méthodes qualitatives en universalité KPZ

24-28 April 2017
Random Walks in Random Environment (1802)
Marches aléatoires en environnement aléatoire

22-26 May 2017
Ising Model Fog Drip, II: the Puddle (1800)
05-26 February 2017
Intermediate Disorder and Weak Universality for KPZ Equation (1803)
15 April – 23 April 2017
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Invités du semestre