Self-interacting Random Walks and Statistical Physics

What it is about

You will learn methods for the analysis of self-interacting random walks and their connections to statistical physics. In the end you will be able to understand and apply central models (e.g. edge-/vertex-reinforced processes), proofs of localization/delocalization, and connections to supersymmetric sigma models and random Schrödinger operators.

What you will be able to do

• Understand simple urn models and concepts of exchangeability
• Knowledge of Edge-Reinforced Random Walk (ERRW) and Vertex-Reinforced Jump Process (VRJP)
• Understanding of the connection to Supersymmetric Hyperbolic Sigma Models
• Insights into Random Schrödinger Operators (if covered)
• Familiarity with proofs of localization and delocalization (various dimensions, strength regimes)
• Application of Ray-Knight/Dynkin localization approaches
• Recognize localization on finite subsets (VRRW, SERRW, “stuck walks”)
• Understanding of phase transitions in reinforced random walks on trees (if time)

What the module consists of

• VorlesungPresentation of content, demonstrative examples and discussion to stimulate independent literature work

Teaching method

• VorlesungConveying content through lecture and examples; discussions aim to motivate independent analysis and further study