Announcing the annual workshop!
See you on 25/04/2025 at the Institut Pascal in Orsay for a day of talks resuming the three topics of this year.
Infos and registration: here
Universality of fully parked trees and catalytic equations
byNicolas Curien
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.