Random Quadratic Form with random forcing: Metastable synchronization by noise

Excerpt

arXiv:2608.16664v1 Announce Type: cross Abstract: We study the Random Quadratic Form (RQF) on a sphere in the presence of random Brownian forcing. We show that the forcing does not effectively change the law of the process but affects the synchronization properties of the system. While the RQF without forcing exhibits partial synchronization due to the intrinsic symmetries, the introduction of an arbitrarily small forcing results in long-term symmetry breaking and leads to full synchronization.