Probabilistic methods for stationary problems of linear transport theory

The steady state of a system of independent particles which undergo elastic collisions can be expressed in terms of the absorption probabilities of the associated Markov process. For the slab albedo problem, this representation enables the application of probabilistic methods to obtain explicit upper and lower bounds on the steady-state density. In particular, the bounds prove the 1/L, decrease of the steady-state flux as a function of the slab widthL (Fick's law).Supported in part by U.S. National Science Foundation grant MCS 75-21684 A02.On leave of absence from Fachbereich Physik, UniversitÄt Mönchen. Work supported by a DFG research fellowship.