The Kardar-Parisi-Zhang Equation and Universality Class (2013)
February 24-March 2, 2013
Organizers: Alexei Borodin, Jeremy Quastel, Herbert Spohn
The Kardar-Parisi-Zhang equation is a nonlinear stochastic partial differential equation widely used in the physics literature as a model of randomly growing interfaces, but until recently very poorly understood from the mathematical point of view. In one dimension, it is a member of a large universality class containing directed random polymers, stochastic Hamilton-Jacobi-Bellman equations, stochastically perturbed reaction-diffusion equations, stochastic Burgers equations and interacting particle models. The class is characterized by the unusual dynamic scaling exponent z=3/2. A number of breakthroughs about 10 years ago led to exact distributions of fluctuations for a few models, with conjectural extrapolation to the whole class. The distributions, surprisingly, turned out to be those recently discovered in random matrix theory. In the last few years there have been a second group of breakthroughs. Several models with adjustable asymmetry have recently been solved through which one can obtain, by scaling limits, exact distributions for various initial conditions for the KPZ equation itself. In addition, there have been breakthroughs in the well-posedness of the KPZ equation.
The goal of this workshop is to build on these advances in two directions. 1. Studying the integrability properties and statistics of the KPZ equation, as well as other models in the KPZ universality class. 2. Extending the universality of the KPZ equation. The new well-posedness theory should provide a route to proving scaling limits to the KPZ equation for a wider class of physical models.
Participants
Fedor Bogomolov, NYU/Courant
Mark Adler, Brandeis University
Gerard Ben Arous, NYU/Courant
Alexei Borodin, MIT
Pasquale Calabrese, Universita di Pisa
Reda Chhaibi, Universitat Zurich
Ivan Corwin, MIT/Microsoft Research
Percy Deift, NYU/Courant
Victor Dotsenko, University of Paris 6
Patrik Ferrari, University of Bonn
Alan Hammond, University of Oxford
Kurt Johnasson, KTH
Kostya Khanin, University of Toronto
Pierre Le Doussal, ENS, Paris
Pierre van Moerbeke, Université catholique de Louvain
Neil O’Connell, Warwick University
Jeremy Quastel, University of Toronto
Tomohiro Sasamoto, Chiba University
Timo Seppalainen, University of Wisconsin-Madison
Senya Shlosman, University of Marseilles
Herbert Spohn, Technische Universitat Munchen
Craig Tracy, UC Davis
Jon Warren, Warwick University