  In this paper we prove that the spatially homogeneous Landau equation for
Maxwellian molecules can be represented through the product of two elementary
processes. The first one is the Brownian motion on the group of rotations. The
second one is, conditionally on the first one, a Gaussian process. Using this
representation, we establish sharp multi-scale upper and lower bounds for the
transition density of the Landau equation, the multi-scale structure depending
on the shape of the support of the initial condition.
