Modelling the interaction of stochastic systems with electromagnetic fields

The analysis presented in this paper, shows how the basic statistics in the interaction of stochastic systems with electromagnetic fields, i.e., the average and the variance of linear observables, can be computed from the probability distributions defining the stochastic geometry. The most difficult part in this computation is the construction of the covariance operator which requires the solution of a series of integral equations over the average geometry. The RHSs of these integral equations are determined by an expansion of the covariance operator of a regular field trace on the stochastic geometry. This determines the computational complexity of the probabilistic approach. In the presentation of this paper, some numerical experiments on concrete examples are shown, and the computational complexity of the probabilistic approach are investigated whether it also determines the minimal computational effort of the statistical approach