Tree-like random metric spaces seen as fixed points of distributional equations

schedule le lundi 30 novembre 2020 de 17h00 à 18h00

Organisé par : E. Bodiot, L. Broux, T. Randrianarisoa, G. Buriticá, Y. Tardy

Intervenant : Lucas Iziquel (LPSM)
Lieu : Online at Zoom: https://zoom.us/j/91323368197?pwd=N3M0d2k3WHE4Tk5adXJ4aHJOWjNhZz09

Sujet : Tree-like random metric spaces seen as fixed points of distributional equations

Résumé :

When studying the scaling limits of some models of random trees or graphs, we obtain random compact metric spaces. From the study of the Continuum Random Tree (CRT), a classical example of such random spaces, we will use its self-similarity property - a well-chosen subspace of the CRT has the same distribution as a rescaled copy of the entire CRT itself - to see the CRT as a fixed-point of a particular equation. From there we will introduce a framework to study this kind of distributional fixed-point equations, the existence and uniqueness of the fixed-points, and the possible convergence towards these fixed-points. Moreover, some geometric properties of the fixed-point can be deduced directly from the equation, for instance its almost sure fractal dimensions. 

Image: A realization of the 1.07-stable looptree from the website of Igor Kortchemski


A realization of the 1.07-stable looptree from the website of Igor Kortchemski