KPZ Universality and Directed Polymers
Universalité de KardarParisiZhang et polymères dirigés
JanuaryJune 2017
Universalité de KardarParisiZhang et polymères dirigés
JanuaryJune 2017
THEMES
The theory of directed polymers and KardarParisiZhang (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, socalled polymer measure, or a single actionminimizing 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 TracyWidom 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 nontrivial 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.

LAUREATES
Local Project Leader
> Prof. Senya SHLOSMAN CNRS, Centre de physique théorique AixMarseille Université 
SCIENTIFIC PROGRAMME
Click on the blue button to find out detailed information on each event.
Random Structures in Statistical Mechanics and Mathematical Physics (1559)
Structures aléatoires en mécanique statistique et physique mathématique 610 March 2017 
Qualitative Methods in KPZ Universality (1558)
Méthodes qualitatives en universalité KPZ 2428 April 2017 
Random Walks in Random Environment (1802)
Marches aléatoires en environnement aléatoire 2226 May 2017 
Ising Model Fog Drip, II: the Puddle (1800)
0526 February 2017 
Intermediate Disorder and Weak Universality for KPZ Equation (1803)
15 April  23 April 2017 
Guests in residence during the semester
Invités du semestre 
VIDEOS
SPONSORS