On some random integral operators generated by an Arratia flow

A. A. Dorogovtsev, Ia. A. Korenovska, E. V. Glinyanaya
Theory of Stochastic Processes
Vol.22 (38), no.2, 2017, pp.8-18
We study some properties of a random integral operator in L2(R) whose kernel is generated by a stationary point process related to an Arratia flow. To prove that this random operator is not bounded we estimate the rate of growth of the maximal amount of clusters in Arratia flow on intervals of unit length.