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

According to first principle quantum mechanics, the evolution of N fermions (particles with antisymmetric wave function) is governed by the many body Schroedinger equation. We are interested, in particular, in the evolution in the mean field regime...

We consider an harmonic chain perturbed by an energy conserving noise and show that after a space-time rescaling the energy-energy correlation function is given by the solution of a skew-fractional heat equation with exponent 3/4.

We prove that the logarithm of Fourier series with random signs is integrable to any positive power. We use this result to prove the angular equidistribution of the zeros of entire functions with random signs (and more generally the almost sure...

I will describe several properties (structural and/or computational) which are satisfied by random matrices almost surely, but for which we have no concrete examples of such matrices. My hope is that the audience will be intrigued and interested in...

I will present recent results on a non-relativistic Hamiltonian model of quantum friction, about the motion of an invading heavy tracer particle in a Bose gas exhibiting Bose Einstein condensate. We prove the following observations: if the initial...

We review some of the connections, established and expected between random matrix theory and Zeta functions. We also discuss briefly some recent Universality Conjectures connected with families of L-functions.

I will present results on the study of various temporal correlation functions of a tagged particle in a one-dimensional system of interacting particles evolving with Hamiltonian dynamics and with initial conditions chosen from thermal equilibrium.

In the 90's numerical simulations have unveiled interesting properties of random ensembles of constraint satisfaction problems (satisfiability and graph coloring in particular). When a parameter of the ensemble (the density of constraints per...

The (weakly) self-avoiding walk is a basic model of paths on the d-dimensional integer lattice that do not intersect (have few intersections), of interest from several different perspectives. I will discuss a proof that, in dimension 4, the...

We will describe formulas for the asymmetric simple exclusion process (ASEP) starting from half-flat and flat initial data. The formulas are for the exponential moments of the height function associated with ASEP. They lead to explicit formulas for...