A rigidity property of superpositions involving determinantal processes

Abstract

The main result of this paper states that if $(N,\Pi )$ is a pair of independent point processes on a common ground space with $N$ Poisson and $\Pi$ determinantal induced by a locally trace class (not necessarily self-adjoint) correlation kernel, then their independent superposition $N+\Pi$ determines uniquely the distributions of $N$ and $\Pi$.

arXiv comment7 pages