Non-equilibrium Dynamics and Random Matrices (nedrm)

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...

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...

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...

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...