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

BENEFICIARIES

SCIENTIFIC PROGRAMME
Research School: Random Structures in Statistical Mechanics and Mathematical Physics (1559)
610 March 2016 
Conference: Qualitative Methods in KPZ Universality (1558)
2428 April 2017 
Small Group: Random Walks in Random Environment (1802)
2226 May 2017 
Research in Pairs I: Ising Model Fog Drip, II: the Puddle (1800)
0526 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
JeanMorlet 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@cirmmath.fr / Tel: +33 (0)4 91 83 30 34
JeanMorlet 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@cirmmath.fr / Tel: +33 (0)4 91 83 30 34