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Mean field variation in random media

1970
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Quarterly of Applied Mathematics
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We consider here the basic equation = p(x), dXi where e(x) is a random function of position and p(x) is a prescribed source term. A formal equation is derived that governs |(x)}, where the braces indicate an ensemble average. The equation, which depends on the boundary conditions of the stochastic problem, is presented in terms of an infinite sequence of correlation functions associated with e(x). The equation is investigated first for the case of an infinite dielectric where isotropy may be

doi:10.1090/qam/266324
fatcat:mx66a4qlrzad3mtgldr6irbmoa