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The height of the infection tree
Consider an SIR model on the complete graph starting with one infected vertex and n healthy vertices. We draw an edge between two vertices when one infects another. What does the tree look like at the end of the epidemic? This kind of tree fits into the framework of uniform attachment trees with freezing, a model of random trees which generalises uniform attachment trees where, besides the uniform attachment mechanism, we introduce a “freezing” mechanism where new vertices cannot attach to frozen vertices. We obtain the scaling limit of the total height of the infection tree depending on the infection rate. The asymptotic behaviour of the total height satisfies a phase transition of order 2. This talk is based on a joint work with Igor Kortchemski and Delphin Sénizergues.
Date:
9 February 2026, 14:00
Venue:
Mathematical Institute, Woodstock Road OX2 6GG
Venue Details:
L5
Speaker:
Emmanuel Kammerer (University of Cambridge)
Organising department:
Department of Statistics
Organisers:
Matthias Winkel (Department of Statistics, University of Oxford),
Julien Berestycki (University of Oxford),
Christina Goldschmidt (Department of Statistics, University of Oxford),
James Martin (Department of Statistics, University of Oxford)
Part of:
Probability seminar
Booking required?:
Not required
Audience:
Public
Editor:
Christina Goldschmidt
