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Sascha Troscheit: Quasi-isometries between Galton-Watson trees

Time: Tue 2025-03-18 13.15 - 14.15

Location: KTH, 3721, Lindstedsvägen 25

Participating: Sascha Troscheit (Uppsala University)

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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.