Andreas Klippel (TU Darmstadt) – Loops vs. Percolation
- Date
- @ Clothworkers South Building LT 3, 14:00
- Location
- Clothworkers South Building LT 3
- Speaker
- Andreas Klippel
- Affiliation
- TU Darmstadt
- Category
- Probability
In recent years, many models in mathematical physics have been encoded into graphical models, which are more accessible through the lens of probability theory. These graphical models often exhibit a natural percolation structure. One such model is the Random Loop Model introduced by Daniel Ueltschi. Peter Mühlbacher showed that the loop threshold for the Random Loop Model with θ=1 is larger than the percolation threshold. This is due to so-called blocking events in graphs with uniformly bounded degree. The proof primarily relies on a coupling method.
In my talk, I will introduce the model and the basic proof techniques. Furthermore, I will discuss a recent result where we generalize the method to obtain new results for general trees.
I will explain why the tree case differs from the case of a general graph. If time permits, I will use the Galton-Watson case to illustrate how the coupling in the proof works.
This talk is based on joint work with V. Betz, M. Kraft, B. Lees and C. Mönch