Random Quadratic Form on a Sphere: Synchronization by Common Noise

Excerpt

arXiv:2603.06187v2 Announce Type: replace-cross Abstract: We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While the one-point dynamics of the system is a Brownian motion and thus has no preferred direction, the two-point motion exhibits nontrivial synchronizing behaviour. In this work we study synchronization of the RQF, namely we give both distributional and path-wise c