The law of thin processes: a law of large numbers for point processes (2502.14839v1)

Abstract: If you take a superposition of n IID copies of a point process and thin that by a factor of 1/n, then the resulting process tends to a Poisson point process as n tends to infinity. We give a simple proof of this result that highlights its similarity to the law of large numbers and to the law of thin numbers of Harremo\"es et al.