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Condensation Phenomena in Random Trees
Last Updated: 2026-02-05 16:37:23
Abstract
Limit theorems for random walks and random trees
Objective
Consider a population that undergoes asexual and homogeneous reproduction over time, originating from a single individual and eventually ceasing to exist after producing a total of n individuals. What is the order of magnitude of the maximum number of children of an individual in this population when n tends to infinity? This question is equivalent to studying the largest degree of a large Bienaymé-Galton-Watson random tree. The goal of the course is to identify a regime where a condensation phenomenon occurs, in which the second greatest degree is negligible compared to the greatest degree. The use of the "one-big jump principle" of certain random walks will be a key tool for studying this phenomenon. Finally, we shall discuss applications of these results to other combinatorial models.
Resources
Lecture Notes
will be available in electronic form
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- MSC
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Condensation Phenomena in Random Trees |
|
2 h weekly |
Offered In
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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