Michel Pain (NYU/Courant)

Title: Precise asymptotics for the height of weighted recursive trees

Abstract: Weighted recursive trees (WRT) are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Recently, Delphin Sénizergues used branching random walk methods to describe the profile of WRT and proved that their height behaves asymptotically as a constant multiple of log(n) under certain regularity assumptions for the weights. In this talk, I will present a future work with Delphin Sénizergues where we obtained the second and third order for the height, proving that the behavior is similar to one appearing for the maximum of a branching random walk. I will present the main ideas of the proof, comparing them with the branching random walk case.

Link: https://mcgill.zoom.us/j/97093259428?pwd=d25yR0J6WGViSzFZOE5rT01YZnBJQT09

Meeting ID: 970 9325 9428

Passcode: problab