Strong Recovery In Group Synchronization

Authors

Bradley Stich, University of North Carolina at CharlotteFollow

Abstract

The group synchronization problem is to estimate unknown group elements at the vertices of a graph when given a set of possibly noisy observations of group differences at the edges. We consider the group synchronization problem on finite graphs with size tending to infinity, and we focus on the question of whether the true edge differences can be exactly recovered from the observations (i.e., strong recovery). We prove two main results, one positive and one negative. In the positive direction, we prove that for a sequence of synchronization problems containing the complete digraph along with a relatively well behaved prior distribution and observation kernel, with high probability we can recover the correct edge labeling. Our negative result provides conditions on a sequence of sparse graphs under which it is impossible to recover the correct edge labeling with high probability.

Author Bio

Bradley Stich is a third-year student at the University of North Carolina at Charlotte studying Mathematics. He conducted this research during a summer undergraduate research experience at UNC Charlotte under the direction of Kevin McGoff and funded by NSF grant DMS-1847144.

Faculty Sponsor

Dr. Kevin McGoff

Recommended Citation

Stich, Bradley (2023) "Strong Recovery In Group Synchronization," Rose-Hulman Undergraduate Mathematics Journal: Vol. 24: Iss. 1, Article 2.
Available at: https://scholar.rose-hulman.edu/rhumj/vol24/iss1/2