Kac's process and the spatially homogeneous Boltzmann equation

Kac introduced a family of stochastic, many particle systems which model the behaviour of a spatially homogeneous, dilute gas, with evolution through binary elastic collisions. In the limit where the number of particles diverges, the empirical measures have the spatially homogeneous Boltzmann equation as a fluid limit. Although the Boltzmann equation itself is not explicitly probabilistic, we may use Kac’s process to study the Boltzmann Equation and vice versa, and in this talk I will discuss some recent works exploring this connection. This talk will also provide a preview of some of the topics I intend to discuss in more detail in the mini-course on the Boltzmann equation.