Investigation of the overexponential growth of the mean particles flux with multiplication in a random medium

A new correlative-grid approximation of a homogeneous and isotropic random density field is introduced for the effective numerically-analytical investigation of overexponential growth of the mean particles flux in a random medium with multiplication. In this case the complexity of the particle trajectory realization is not dependent on the correlation scale. For the correlative-grid approximation the possibility of a Gaussian asymptotics of the mean particles multiplication rate is justified for a random field of bounded density. It ensures a superexponential growth of the flux in some initial time interval. An estimate of further overexponential flux growth is constructed based on some test computations.