[ABE-L] Seminário de Probabilidade do IM - UFRJ - 01/09/2025

[Maria Eulalia Vares]

Dear colleagues,



Our next seminar will be held on Monday, *September 1*, from *3:30 p.m. to
4:30 p.m*. (Rio de Janeiro local time).

It will be held through Google Meet *https://meet.google.com/idy-jhss-htx*
<https://meet.google.com/idy-jhss-htx>



Speaker: *  Minmin Wang (University of Sussex)*

Title: *Exchangeability in Continuum Random Trees*

Abstract: De Finetti’s Theorem states that all N-indexed exchangeable
sequences of real-valued random variables are mixings of i.i.d sequences.
For real-valued random processes with exchangeable increments on [0, 1],
Kallenberg’s 1973 result provides a complete characterisation of these
processes via another mixing relationship.

Continuum random trees are random tree-like metric spaces that arise
naturally as scaling limits of various models of discrete random trees. In
this talk, we will focus in particular on two subclasses of continuum
random trees: the so-called stable trees and inhomogeneous continuum random
trees. An analogue of Kallenberg’s Theorem for continuum random trees first
appeared as a claim in a 2004 paper by Aldous, Miermont and Pitman. They
suggested that, in much the same way that a stable bridge process on [0, 1]
is a mixing of certain extremal exchangeable processes, stable trees are
mixings of inhomogeneous continuum random trees.

We present an outline of a rigorous argument supporting this claim, based
on a novel construction that applies to both classes of trees. We will also
briefly discuss some implications of this result on critical random graphs.

The talk is based on the paper *Stables trees as mixings of inhomogeneous
continuum random trees,* Stochastic Processes and their Applications 175,
2024, 104404.

More complete information about the seminars can be found at

https://ppge.im.ufrj.br/seminarios-de-probabilidade/

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares

-- 
Maria Eulalia Vares
Professora Titular - Instituto de Matemática - UFRJ
Coordenadora do Programa de Pós-Graduação em Estatística
https://ppge.im.ufrj.br/
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