Seminar: Random interlacements

Sommer semester 2018

Prof. Dr. Silke Rolles

• Time and location: Thursday, 14:00-15:30, in MI 03.12.020A. The seminar will take place weekly.
• First talk: Thursday, April 19, 2018.
• Prerequisites: Probability theory (MA2409) and interest in the subject.
• Content: Random interlacements were introduced by Sznitman in 2007. By now, they form a very active area of research. The random interlacement process is a Poisson process consisting of doubly infinite trajectories of a random walk. The seminar gives an introduction to this exciting subject.
• Literature: Alexander Drewitz, Balazs Rath and Artem Sapozhnikov: An Introduction to Random Interlacements, Springer briefs in mathematics, 2014. ebook
• A guide how to present a talk: Manfred Lehn: Wie halte ich einen Seminarvortrag 
• List of talks:
  1. Chapter 1: Random walk, Green function and equilibrium measure
  2. Chapter 2: Random interlacements: first definition and basic properties
  3. Chapter 3: Random walk on the torus and random interlacements
  4. Chapter 4: Poisson point processes and Chapter 5, Section 5.1.1
  5. Chapter 5: Random interlacement point process starting with Section 5.1.2
  6. Chapter 6: Percolation of the vacant set
  7. Chapter 7: Source of correlations and decorrelation via coupling
  8. Chapter 8: Decoupling inequalities
  9. Chapter 9: Phase transition