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.

SRGS_Revised.pdf (277 kB)
Revised Submission

SRGS_Revised.zip (15 kB)
Latex Source Files

ResponseSRGS.pdf (172 kB)
Response to the Review

SRGS_Revised (1).zip (19 kB)
Latex Source Files (Second Revision)

Included in

Probability Commons