Qualitative Methods in KPZ Universality (1558)
Méthodes qualitatives dans l’universalité KPZ

Dates: 24-28 April 2017 at CIRM (Marseille Luminy, France)

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.​


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

Multi-time distribution of periodic TASEP​ (pdf)

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

On the Gibbs property for determinantal point processes​

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

The ASEP and Hall-Littlewood Gibbsian line ensembles

Discretisation of regularity structures

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

Tilings and non-intersecting paths beyond integrable cases

Weak universality of the KPZ equation with arbitrary nonlinearities

Low temperature interfaces and level lines in the critical prewetting regime

Large deviations for certain inhomogeneous corner growth models (pdf)

Stationary random walks on the lattice​

The KPZ fixed point

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

Martingale solutions to the KPZ equation (pdf)

TASEP in continuous inhomogeneous space

Local Behavior of Airy Processes (pdf)

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

Variational formulas and geodesics for percolation models

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

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

High temperature limits of directed polymers with heavy tail disorder