Previous Special Year Seminar

Many of the major results of modern ergodic theory can be understood in terms of a sequence of finite metric measure spaces constructed from the marginal distributions of a shift-invariant process. Most simply, the growth rate of their covering...

We present the key ideas of a new proof of Landau damping for the Vlasov-Poisson equation obtained in a joint work with Bedrossian and Masmoudi. This nonlinear transport equation is a fundamental model for describing self-interacting plasmas or...

We consider a typical situation in which probability model itself has non-negligible cumulated uncertainty. A new concept of nonlinear expectation and the corresponding non-linear distributions has been systematically investigated: cumulated...

Free entropy is a quantity introduced 20 years ago by D. Voiculescu in order to investigate noncommutative probability spaces (e.g. von Neumann algebras). It is based on approximation by finite size matrices. I will describe the definition and main...

We consider two classes of \(n \times n\) sample covariance matrices arising in quantum informatics. The first class consists of matrices whose data matrix has \(m\) independent columns each of which is the tensor product of \(k\) independent \(d\)...

I will explain how Pitman's theorem on Brownian motion and the three dimensional Bessel process can be extended to several dimensions, and the connection with random matrices, and combinatorial representation theory, notably the Littelmann path...

We discuss some properties of a version of the one-dimensional totally asymmetric zero-range process in which a particle hops to the nearest neighbor site with rate proportional to \(1-q^n\), with \(n\) being the number of particles at the site. The...