We re happy to announce two new papers by our group members.
The paper "Fast and Slow Mixing of the Kawasaki Dynamics on Bounded-Degree Graphs" was written by Aiya Kuchukova, Marcus Pappik, Will Perkins and Corrine Yap and will be published in the RS&A journal.
The authors study the worst-case mixing time of the Kawasaki dynamics for the fixed magnetization Ising model on bounded-degree graphs, relating it to various phase transition thresholds of the grand-canonical Ising model. The main result is to partially disprove a conjecture by Carlson, Davies, Kolla and Perkins by showing that, above the tree uniqueness threshold, the magnetization regime in which Kawasaki dynamics are rapidly mixing is strictly smaller than the tractable regime. An extended abstract of this paper was previously published at the conference RANDOM 2024.
Furthermore, we like to introduce you to the paper "Optimal Padded Decomposition for Bounded Treewidth Graphs" written by Arnold Filtser, Tobias Friedrich, Davis Issac, Nikhil Kumar, Hung Le, Nadym Mallek and Ziena Zeif published in the journal TheoretiCS.
Padded decompositions have been studied for decades and have had serious implications for many fundamental problems. They aim at obtaining a stochastic decomposition of a graph into clusters of diameter at most ẟ that satisfy some other given properties. This paper answers positively a 30 years old famous conjecture about bounded treewidth graphs and their padded decompositions.
