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Thesis

Recursive construction of continuum random trees and some contributions to the theory of tree-valued stochastic processes

Abstract:

We introduce a general recursive method to construct continuum random trees (CRTs) from i.i.d. copies of a string of beads, that is, any random interval equipped with a random discrete measure. We prove the existence of these CRTs as a new application of the fixpoint method formalised in high generality by Aldous and Bandyopadhyay. We further apply this recursive construction to "embed" Duquesne and Le Gall's stable tree into a binary compact CRT in a way that solves an open problem p...

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Grant:
EP/P505666/1
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Type of award:
DPhil
Awarding institution:
University of Oxford

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