Seminar: Processes with reinforcement

Sommer semester 2020

Prof. Dr. Silke Rolles

• Time and location: The seminar takes place weekly via zoom. More details are given in moodle.
• First talk: During the first week of teaching.
• Prerequisites: Probability theory (MA2409) and interest in the subject.
• Content: Stochastic processes with reinforcement are a very active area of research. The literature on the subject has been growing tremendously during the past 20 years. In the seminar, we will have a look at various important models. These include urn models, edge-reinforced random walks, vertex-reinforced random walk, processes in discrete and in continuous time. The common feature are random transition probabilities. They can change over time or they can be sampled before the motion starts. This exciting subject gives many opportunities to write a bachelor's or master's thesis.
• Literature:
  • Some talks will be based on the book Norman Lloyd Johnson and Samuel Kotz: Urn models and their application: an approach to modern discrete probability theory, Wiley, 1977.
  • Furthermore, we will study the following research articles.
    1. Jiro Akahori, Andrea Collevecchio, Masato Takei: Phase transitions for edge-reinforced random walks on the half-line pdf 
    2. Erich Baur: On a class of random walks with reinforced memory pdf 
    3. Jean Bertoin: Noise reinforcement for Lévy processes pdf 
    4. Xinxin Chen, Xiaolin Zeng: Speed of Vertex reinforced jump process on Galton-Watson trees pdf 
    5. Dirk Erhard, Tertuliano Franco and Guilherme Reis: The Directed Edge Reinforced Random Walk: The Ant Mill Phenomenon pdf 
    6. Daniel Kious, Bruno Schapira and Arvind Singh: Once reinforced random walk on Z×Γ pdf 
    7. Yevgeniy Kovchegov: Multi-particle processes with reinforcements pdf 
    8. Christophe Sabot, Pierre Tarrès, and Xiaolin Zeng: The Vertex Reinforced Jump Process and a Random Schrödinger operator on finite graphs pdf 
    9. Bruno Schapira: Localization on 5 sites for vertex reinforced random walks: Towards a characterization pdf 
• A guide how to present a talk: Manfred Lehn: Wie halte ich einen Seminarvortrag 
• Schedule of talks: to be announced