Special Year 2013-14: Non-equilibrium Dynamics and Random Matrices - Seminar

We prove a quantitative Brunn-Minkowski inequality for sets \(E\) and \(K\), one of which, \(K\), is assumed convex, but without assumption on the other set. We are primarily interested in the case in which \(K\) is a ball. We use this to prove an...

The stochastic Burgers equation (equivalent to the one-dimensional KPZ equation) is a hyperbolic conservation law with random currents. In applications, one often has to deal with several conservation laws, a little explored case. We discuss several...

In several naturally occurring (infinite) point processes, we show that the number (and other statistical properties) of the points inside a finite domain are determined, almost surely, by the point configuration outside the domain. This curious...

I will describe the general ideas behind exponential asymptotic methods, their recent developments, and a number of open problems that were solved in the last few years using them, such as the behavior of Hydrogen atoms in time periodic fields and...

After a short introduction to some ideas on quantum probability theory I discuss the roles played by loss of information and entanglement in the emergence of facts in quantum-mechanical experiments and observations. Besides explaining why...

This will be an informal session in which we will try to answer questions from the audience on topics around KPZ.

We discuss two random decreasing sequences of continuous functions in two variables, and how they arise as the scaling limit from corners of a (real / complex) Wigner matrix undergoing stochastic evolution. The restriction of the second one to...

We construct a \(\mathrm{KPZ}_t\) line ensemble -- a natural number indexed collection of random continuous curves which satisfies a resampling invariance called the H-Brownian Gibbs property (with \(H(x)=e^x\)) and whose lowest indexed curve is...

Inspired by recent work of Alberts, Khanin and Quastel, we formulate general conditions ensuring that a sequence of multi-linear polynomials of independent random variables (called polynomial chaos expansions) converges to a limiting random variable...

I will discuss the proof by Yang Kang and myself of diffusion for the Markov Anderson model, in which the potential is allowed to fluctuate in time as a Markov process. However, I want to highlight the method of the proof more than the result itself...