Universality of Kardar-Parisi-Zhang (KPZ) scalings is one the most active areas in statistical mechanics and mathematical physics in the last 10 years. 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. This can be done only for specific exactly integrable models. However, it is expected that universality holds for extremely general class of disordered systems in dimension 1+1. It is a very rare case when highly non-trivial scaling behaviour describes both zero temperature (geodesics in random metric, first (last) passage percolation, action minimizing paths and positive temperature regimes. Despite very clean and concrete predictions and a wide belief in the validity of the conjectures, there has been very little progress in our understanding of the problem of universality. The proposed workshop will concentrate on qualitative methods which are applicable in a very general situation. One of the strategies is based on the analysis of global solutions to the random Hamilton-Jacobi equation.

The main goal is to prove that the stationary Busemann function will have diffusive behaviour which implies KPZ scalings. Another direction is related to stability analysis for renormalization fixed point corresponding to Airy process.

Most of the meetings in this area are dealing with exact formulas and exactly solvable models. The proposed workshop is the first one which aims to concentrate on the problem of universality.​

• Tom Alberts (University of Utah)
• Yuri Bakhtin (Courant Institute)
• Eric Cator (Radboud University)
• Dmitry Dolgopyat (University of Maryland)
• Konstantin Khanin (University of Toronto & Aix-Marseille Université)
• Jeremy Quastel (University of Toronto)
• Senya Shlosman (CNRS, Aix-Marseille Université)

• Amol Aggarwal (Harvard University)

Current Fluctuations of the Stationary ASEP and Six-Vertex Model (pdf)

• Jinho Baik (University of Michigan) – VIDEO

Multi-time distribution of periodic TASEP​ (pdf)

• Guillaume Barraquand (Columbia University)

ASEP on a half-space with an open boundary and the KPZ equation in a half space (pdf)

• Alexander Bufetov (CNRS, Aix-Marseille Université)

On the Gibbs property for determinantal point processes​

• Francis Comets (Université Paris Diderot)

Mean-field directed polymers on an open graph (pdf)

• Evgeni Dimitrov (MIT)

The ASEP and Hall-Littlewood Gibbsian line ensembles

• Dirk Erhard (University of Warwick)

Discretisation of regularity structures

• Patrik Ferrari (Bonn University)

Universality of the GOE Tracy-Widom distribution for TASEP with arbitrary particle density

• Vadim Gorin (MIT) – VIDEO

Tilings and non-intersecting paths beyond integrable cases

• Martin Hairer (University of Warwick) – VIDEO

Weak universality of the KPZ equation with arbitrary nonlinearities

• Dmitry Ioffe (Technion, Israel Institute of Technology) – VIDEO

Low temperature interfaces and level lines in the critical prewetting regime

• Christopher Janjigian (Université Paris Diderot)

Large deviations for certain inhomogeneous corner growth models (pdf)

• Arjun Krishnan (University of Utah)

Stationary random walks on the lattice​

• Konstantin Matetski (University of Toronto)

The KPZ fixed point

• Hirofumi Osada (Kyushu University)

Interacting Brownian motions in infinite dimensions with logarithmic potentials and Airy point process

• Nicolas Perkowski (Humboldt-Universität zu Berlin)

Martingale solutions to the KPZ equation (pdf)

• Leonid Petrov (University of Virginia)

TASEP in continuous inhomogeneous space

• Leandro Pimentel (Universidade Federal do Rio de Janeiro)

Local Behavior of Airy Processes (pdf)

• Firas Rassoul-Agha (University of Utah)

KPZ wandering exponent for random walk in i.i.d. dynamic Beta random environment (pdf)

• Timo Seppäläinen (University of Wisconsin Madison)

Variational formulas and geodesics for percolation models

• ​Fabio Toninelli (CNRS, Université Lyon 1) – VIDEO

A 2d growth model in the anisotropic KPZ class (pdf)

• Ke Zhang (University of Toronto)

Hyperbolicity of minimizers and Random Hamilton-Jacobi equations (pdf)

• Nikos Zygouras (University of Warwick)

High temperature limits of directed polymers with heavy tail disorder