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In this paper we prove that the spatially homogeneous Landau equation forMaxwellian molecules can be represented through the product of two elementaryprocesses. The first one is the Brownian motion on the group of rotations. Thesecond one is, conditionally on the first one, a Gaussian process. Using thisrepresentation, we establish sharp multi-scale upper and lower bounds for thetransition density of the Landau equation, the multi-scale structure dependingon the shape of the support of the initial condition.

The Landau Equation for Maxwellian molecules and the Brownian Motion on SO_R(N)