A reading group towards Self-similar Markov trees and scaling limits

Time: 11.15am on Mondays (Weeks 1 to 8).
Place: Department of Statistics, Seminar Room LG.04 (Weeks 1, 2, 4, 6, 8), Meeting Room 3 (3rd floor) (Weeks 3, 5), Small Lecture Theatre LG.03 (Week 7).

The aim of this reading group is to work towards reading the recent preprint "Self-similar Markov trees and scaling limits" which is the first part of a forthcoming monograph by Jean Bertoin, Nicolas Curien and Armand Riera.

Before we start on the paper itself, we plan to cover the necessary background. Topics will include Lévy processes, self-similar Markov processes, scaling limits, Markov branching trees, self-similar fragmentations, branching Lévy processes, before finally turning to the Bertoin-Curien-Riera paper.

All are welcome, but please contact me in advance to let me know you want to participate.

A more detailed plan will appear here in due course!

Week 1: Matthias Winkel, Towards scaling limits of multitype Galton-Watson trees.

Week 2: Mie Glückstad, Infinite divisibility (reading Billingsley "Probability and Measure" (2nd ed) Section 28).

Week 3: David Geldbach, Convergence of random walks to Lévy processes (reading Billingsley "Convergence of Probability Measures" (2nd ed) pages 145-148, online access provided by Bodleian Libraries).

Week 4: Leo Tyrpak, Positive self-similar Markov processes (reading Kyprianou "Fluctuations of Lévy processes" (2nd ed) Section 13.3).

Week 5: Christina Goldschmidt, Markov branching trees, Part I (reading Haas "Scaling limits of Markov branching trees and applications" and Haas and Miermont "Self-similar scaling limits of non-increasing Markov chains", access provided by Bodleian Libraries)

Week 6: Liam Hill, Markov branching trees, Part II (reading Haas "Scaling limits of Markov branching trees and applications" and Haas and Miermont "Scaling limits of Markov branching trees with applications to Galton--Watson and random unordered trees", access provided by Bodleian Libraries)

Week 7: Félix Foutel-Rodier, Growth-fragmentations

Week 8: No reading group this week