Dimers, Double Dimers, and Spatial Permutations with Long-Range Interactions

Link to Join Zoom Meeting

**This talk will be broadcast at 13:30 BT / 14:30 CET / 15:30 EET, February 25th, 2026 on Zoom only. **

Meeting-ID: 667 4776 1513 Passcode: 834059

Abstract

The dimer model and its associated double-dimer model are fundamental objects in probability theory, statistical mechanics, and combinatorics. While their planar behavior is by now well understood, much less is known beyond planarity.

We study these models on $Z^d$-like graphs ($d≥1$), allowing long-range edges whose weights decay with distance. For a large class of such interactions, we show that monomer correlations in the dimer model remain uniformly positive, and that loops in the double-dimer model are macroscopic.

In this talk, I will introduce the models, explain their connection to spatial permutations, and give an overview of the main proof ideas. In particular, we will take a closer look at the key method, namely reflection positivity. The project presented in this talk is joint work with Lorenzo Taggi and Wei Wu.

About Andreas

Andreas is a final-year PhD student at TU Darmstadt, supervised by Volker Betz. Starting in August, he will join Johannes Gutenberg University Mainz as a postdoctoral researcher in the group of Lisa Hartung. His research interests lie at the intersection of statistical mechanics, random graphs, and network theory. Before studying mathematics, he worked as a software engineer at Deutsche Bahn.