Percolation on trees as a Brownian excursion

Nicholas Moloney and Francesc Font-Clos have written up their calculation on the size of percolating clusters in branching processes. They exploit a mapping between continuum trees and Brownian excursions, and arrive at a diffusion equation with suitable boundary conditions. In this way, they provide an intuitive rederivation of results first obtained by Botet and Płoszajczak by other methods.
The article is published in Physical Review E:

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