Graphical methods are often employed in the analysis of multiparticle systems. A particularly interesting example in the context of kinetic theory was introduced by McKean, who developed a formula expressing the exact solution of the spatially homogenous Boltzmann equation for Maxwellian molecules in terms of Wild convolutions and a certain random walk on graphs. Recent work with Carlen, and Gabetta, as well as work by Dolera and Regazinni, has shown that this expression can be exploited to provide very precise estimates on the solutions of the Boltzmann equation. In this talk, we explain some of these results, and the ideas on which they are based.
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