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...
