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
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