Sascha Troscheit: Quasi-isometries between Galton-Watson trees

Abstract:

The Galton-Watson process (and tree) is one of the archetypal random tree constructions. Inspired by the work of Basu, Sidoravicius, and Sly, which established the almost sure bi-Lipschitz equivalence of two independent percolations on the lattice, we prove the almost sure quasi-isometric equivalence of a large family of Galton-Watson trees. This also implies quasi-symmetric equivalence of a large class of stochastically self-similar sets under some separation conditions. The proof has interesting links to the “car-parking problem” on trees which I will also present in this talk. Based on joint work with Jayadev Athreya.