'KPZ Universality and Directed Polymers'
This semester has now ended

SPONSORS

THEMES

_
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.
BENEFICIARIES
Chair
Konstantin KHANIN
University of Toronto
Webpage

Local Project Leader
Senya Shlosman
CNRS, Centre de Physique Théorique
Aix-Marseille Université
Webpage

SCIENTIFIC PROGRAMME

Research School: Random Structures in Statistical Mechanics and Mathematical Physics (1559)
6-10 March 2016
Conference: Qualitative Methods in KPZ Universality (1558)
24-28 April 2017
Small Group: Random Walks in Random Environment (1802)
22-26 May 2017
Research in Pairs I: Ising Model Fog Drip, II: the Puddle (1800)
05-26 February 2017
Research in Pairs II: Intermediate Disorder and Weak Universality for KPZ Equation (1803)
15 April - 23 April 2017

Programme of invitations

Information for Young Researchers interested in attending any event of this semester
CONTACT
Jean-Morlet Chair scientific activities take place at CIRM Luminy.
Centre International de Rencontres Mathématiques (CIRM), 163 Avenue de Luminy, Case 916, 13288 Marseille cedex 9, FRANCE

Coordinator: Ms Céline Montibeller, International Officer.
Email: celine.montibeller@cirm-math.fr / Tel: +33 (0)4 91 83 30 34