Seed Seminar

Mathematics

Universality of fully parked trees and catalytic equations

by

Nicolas Curien

on  April-25-2025, 10:00 ! Livein  Institut Pascalfor  60min
Abstract:

We show that critical parking trees conditioned to be fully parked converge in the scaling limits towards the Brownian growth-fragmentation tree, a self-similar Markov tree different from Aldous’ Brownian tree. As a by-product of our study, we prove that positive non-linear functional equations involving a catalytic variable display a universal polynomial exponent 5/2 at their singularity, confirming a conjecture by Chapuy, Schaeffer and Drmota & Hainzl. Compared to previous analytical works on the subject, our approach is probabilistic and exploits an underlying random walk hidden in the random tree model. Joint work with Alice Contat.

 All talks  Winter '25: Random geometry and quantum gravity