Zoom recording session 1: Senya Shlosman, Yvan Velenik, Patrik Ferrari, Alexey Bufetov.
Zoom recording session 2: Alexandre Gaudillière, Guillaume Barraquand, Sergei Nechaev.

Guillaume Barraquand (Paris), Alexey Bufetov (Leipzig), Bernard Derrida (Paris), Patrik Ferrari (Bonn), Alexandre Gaudillière (Marseille), Sergei Nechaev (Moscow), Senya Shlosman (Moscow & Marseille), Yvan Velenik (Genève),

Guillaume Barraquand (Paris): KPZ equation on the positive real line: invariant measures and fluctuations. pdf

This talk will be about the Kardar-Parisi-Zhang equation on the positive real line, with Neumann type boundary condition at zero. At large time, the solution can be seen as the sum of two terms: (1) A global height shift, diverging with time, whose fluctuations are characterized by a 1/3 exponent and distributions related to random matrix theory. (2) A spatial process asymptotically distributed according to some invariant measure for the KPZ dynamics. Unlike for the KPZ equation on the full-line, invariant measures on a half-line are in general not Brownian, and depend non-trivially on boundary conditions. Inverting a Laplace transform formula recently obtained by Ivan Corwin and Alisa Knizel for invariant measures of the KPZ equation on a segment, we will explain a simple probabilistic description of the half-line invariant measures. We will also review rigorous results and conjectures about large time fluctuations of the solution for various boundary and initial conditions.

Alexey Bufetov (Leipzig): Asymptotics of multi-species ASEP. pdf

Asymmetric simple exclusion process (ASEP) is one of the most studied models of interacting particle systems. It is known to belong to the Kardar-Parisi-Zhang universality class due to pioneering work of Johansson and Tracy-Widom. In this talk I will review some asymptotic results about its multi-species extension, which are based on the interpretation of this process as a random walk on Hecke algebra.

Bernard Derrida (Paris): Renormalization and disorder : a simple toy model. pdf

After a short review of our understanding of how a weak disorder or a low density of impurities affect the universality class of a phase transition, I will discuss a simple tree-like toy model for which one can prove that, due to disorder, the depinning transition becomes an infinite order transition of the Berezinski-Kosterlitz-Thouless type. This toy model was introduced to understand the depinning transition of a line from a random substrate, one of the simplest problems in the theory of disordered systems. This depinning transition has a long history among physicists and mathematicians. Still the nature of the transition, one of the central questions of the problem, remains unsolved.

Patrik Ferrari (Bonn): Fluctuations of shocks in the asymmetric simple exclusion process. pdf

In this talk we consider the totally asymmetric simple exclusion process with different types of initial conditions. We will discuss the different scalings and distribution functions which arises in the large time limits. This talk is based on several papers with Peter Nejjar and a recent work with Alexey Bufetov.

Alexandre Gaudillière (Marseille): A tribute to Francesca Nardi.

Sergei Nechaev (Moscow): Stretching of a fractal polymer near a disc reveals KPZ-like statistics. pdf

We examine stretching of a 2D fractal polymer chain near a disc of radius $R$ and find that excursions of the polymer away from the surface scale as $\Delta \sim R^{\beta}$, with the KPZ growth exponent $\beta=1/3$, for any fractal dimension of the polymer chain. We discuss potential applications of this result as well as its surprising logical and mathematical connections with several branches of mathematical and condensed matter physics, such as 1D Anderson localization and Donsker-Varadhan survival probability of 1D random walk in a Poissonian array of traps.

Senya Shlosman (Moscow & Marseille): A tribute to Dima Ioffe.

Yvan Velenik (Genève): $1/3\,-\,2/3$ scaling in the Ising model. pdf

I'll review several situations in which fluctuations displaying $1/3\,-\,2/3$ scaling appear naturally in the analysis of the planar Ising model.