The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

We analyze the two‐dimensional parabolic‐elliptic Patlak‐Keller‐Segel model in the whole
Euclidean space ℝ2. Under the hypotheses of integrable initial data with finite second …

Statistical mechanics is a powerful method for understanding equilibrium thermodynamics.
An equivalent theoretical framework for nonequilibrium systems has remained elusive. The …

This paper is devoted to the study of propagation of chaos and mean-field limits for systems
of indistinguishable particles, undergoing collision processes. The prime examples we will …

We consider a metric for probability densities with finite variance on ℝ d, and compare it with
other metrics. We use it for several applications both in probability and in kinetic theory. The …

We reckon the rate of exponential convergence to equilibrium both in relative entropy and in
relative Fisher information, for the solution to the spatially homogeneous Fokker-Planck …

We derive a new lower bound for the entropy dissipation associated with the spatially
homogeneous Boltzmann equation. This bound is expressed in terms of the relative entropy …

We analyze the large-time behavior of various kinetic models for the redistribution of wealth
in simple market economies introduced in the pertinent literature in recent years. As specific …

The present notes are intended to present a detailed review of the existing results in
dissipative kinetic theory which make use of the contraction properties of two main families …