Moments of the critical parameters of the transport of particles in a random medium

The problem of estimating the moments of the critical values of transport in a medium with a random density that scatters, absorbs, and multiplies particles is solved. To this end, a special iterative process is used to estimate the first- and second-order derivatives of the critical parameters with respect to the density in different subregions of the medium. These estimates are used to implement linearization and homogenization methods. In addition, a simple probabilistic model of transport in an unbounded medium with the additional absorption probability depending on the random density is constructed. The computation results demonstrate the practical effectiveness of the estimates.