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401-4614-24L 4 Credits MSC D-MATH

Condensation Phenomena in Random Trees

Lecturers & Examiners: Prof. Dr. Igor Kortchemski
VVZ CR n/a

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)

General Information

Language
English
Levels
MSC

Examination

Type
session examination
Mode
oral 20 minutes
Only in Summer 2024. No repetition exam.

Course Components

Type Title Time & Place Hours
lecture Condensation Phenomena in Random Trees
  • Thu 08:15-10:00 (HG D 3.2)
2 h weekly

Offered In