Colloquium: The Boltzmann Equation, Propagation of Chaos and the Kac model

Abstract: Formulated in the second half of the 19th century, the Boltzmann equation has become one of the fundamental equations of statistical physics, and important in many applications. As a bridge between a reversible microscopic world and an irreversible macroscopic world it was controversial from the start. This controversy has been resolved, but from a mathematical point of view the equation is still very challenging. In the talk I will give a background to the equation and focus on problems related to a rigorous derivation from a model of a particle system. This leads to Marc Kac's notion of propagation of chaos and his model of the Boltzmann equation, for which most mathematical problems have been solved.