# Non-equilibrium Dynamics and Random Matrices (nedrm)

### Geometry of metrics and measure concentration in abstract ergodic theory

Tim Austin
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...

### Landau damping: Gevrey regularity and paraproducts

Clément Mouhot
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...

### Nonlinear Brownian motion and nonlinear Feynman-Kac formula of path-functions

Shige Peng
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

Philippe Biane
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...

### Limiting Eigenvalue Distribution of Random Matrices Involving Tensor Product

Leonid Pastur
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 $$d$$...

See agenda