New Monte Carlo algorithms for investigation of criticality fluctuations in the particle scattering process with multiplication in stochastic media

A Monte Carlo algorithm admitting parallelization is constructed for estimation of probability moments of the spectral radius of the operator of the integral equation describing transfer of particles with multiplication in a random medium. A randomized homogenization method is developed with the same aim on the base of the theory of small perturbations and diffusive approximation. Test calculations performed for a one-group spherically symmetric model system have shown a satisfactory concordance of results obtained from two models.