A Markov Process associated to the noncutoff Boltzmann Equation

We consider the stochastic model of an $N$-particle gas due to Kac, introduced as a proxy to the Boltzmann equation, in the case where the intermolecular forces are long-range `hard potentials’. In this case, there is an abundance of grazing collisions: the Markov process is a jump process of constant activity. We introduce a coupling of the $N$-particle Kac processes, and show how this leads to uniqueness and stability for the Boltzmann equation and a law of large numbers.

• Speaker: Daniel Heydecker (Cambridge)
• Tuesday 13 October 2020, 14:00–15:00
• Venue: Zoom.
• Series: Probability; organiser: Perla Sousi.