Gerónimo Uribe (Instituto de Matemáticas-UNAM, Mexico)
On random trees and Lévy type processes
Abstract: The year 1875 marks the introduction of stochastic elements in the modelling of population growth with Galton and Watson´s landmark paper On the Probability of the Extinction of Families.
Fast-forward to 1991 when the Galton-Watson model was reinterpreted as one of random genealogical trees by Aldous. This enabled the construction of a universal scaling limit of discrete Galton-Watson trees via a random metric space with tree-like structure called the Continuum Random Tree.
In this talk, we outline some aspects of random models of discrete trees and of their proven or conjectured scaling limits. Main aims will be the introduction of time in the models in order to distinguish chronology from genealogy and a sample of locally compact random real trees. Lévy processes will play a prominent role.
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