Student Seminar in Probability Theory Spring 2024

Organizers
Igor Kortchemski, Vincent Tassion
Coordinator
Franco Severo
Course Catalogue
401-3600-24L

Seminar

The seminar will take place in-person at HG F 26.5 on Thursdays from 12:15 to 14:00, starting on 22.02

Information meeting

An information meeting has been held on Zoom on December 21st.

  • the recording is available.
  • Slides concerning the organization.

    • Content

    The subject of the Seminar will be: random graphs. They are a fascinating subject at the cross-road of probability, statistical physics, combinatorics and applications. Indeed, random graphs are instrumental in the study of real-world networks. Random graphs pose many beautiful and challenging questions, which we shall explore in the seminar.

    A random tree

    The following topics should be covered:

  • Bienaymé-Galton-Watson trees with applications to uniform plane trees and Cayley trees.
  • Phase transition in Erdos-Renyi (connectivity, size of the maximal component).
  • Degrees in trees built by uniform attachment
  • Local limits of random trees and random maps.

    • Main goals:

  • learn how to communicate and present mathematics orally.
  • Analyze one topic in depth, build own intuition, and structure it suitably for a talk.

    • Talks

    Some tips for your oral presentations.
    Date Speakers Content
    Talk 1:
    February 29     		Finn Michler & Alexander Seidl Coding Bienaymé-Galton-Watson trees by random walks
    Talk 2:
    March 7     		Finn Michler & Alexander Seidl Uniform trees and Cayley trees
    Talk 3:
    March 14     		Laury Verhoeven & Leonard Vetter Erdös-Rényi random graphs: sharp threshold for connectivity
    Talk 4:
    March 21    		 Laury Verhoeven & Leonard Vetter Erdös-Rényi random graphs: size of the maximal connected component
    Talk 5:
    March 28    		 Louis Clayes & Axel Caulier Degree sequence in preferential attachment trees
    Talk 6:
    April 11    		 Louis Clayes & Axel Caulier Maximal degree in preferential attachment trees
    Talk 7: April 18
    		 Katharina Petre Degrees in Erdös-Rényi random graphs
    Talk 8: April 25
    		 Sven Keller & Justus Schilling Local limits of random trees
    Talk 9: May 2
    		 Sven Keller & Justus Schilling Local limits of random maps
    Talk 10: May 16
    		 Nicolas Hotton & Jonathan Wächter The method of moments
    Talk 11: May 23
    		 Nicolas Hotton & Jonathan Wächter Random regular graphs

    Literature