Málstofa í stærðfræði

Fyrirlesari: Benedikt Stufler, École normale supérieure de Lyon

Titill: The asymptotic geometric shape of random combinatorial trees

Staðsetning: TG-227 (Tæknigarður, 2. hæð)
Tími: Föstudagur 27. janúar kl. 13:20

Ágrip:

In his pioneering papers in the early 90s, Aldous established the continuum random tree (CRT) as the scaling limit of random labelled trees. He conjectured that the CRT also arises as scaling limit of trees considered up to symmetry. The convergence of random Pólya trees, that is, unlabelled rooted trees, was confirmed around 20 years later by Haas and Miermont, and we discuss an alternative proof by Panagiotou and the speaker. The second part of the talk treats random unlabelled unrooted trees and discusses a very general result that allows for a transfer of asymptotic properties of rooted trees to unrooted trees, in particular the convergence toward the CRT.