Spectral gap for Kac's model of Boltzmann equation
Résumé
We consider a random walk on S^{n-1}, the standard sphere of dimension n-1, generated by random rotations on randomly selected coordinate planes i, j with 0 < i < j < n+1. This dynamics was used by Marc Kac as a model for the spatially homogeneous Boltzmann equation. We prove that the spectral gap on S^{n-1} is 1/n up to a constant independent of n.