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 \(d\)...