Abstract
A large class of problems in solid-state physics reduces to the investigation of essentially non-Gaussian random fieldsσ(r) generated by identical point sources placed independently at the sites of a three-dimensional lattice. Finite expressions are obtained for all one- and two-point moments of such a field in terms of the concentration of sources and functionals of the Green's function of the source. In the same form, a description is given of the field of an arbitrary polynomial R(σ p) of two fieldsσ 1 andσ 2 generated by the same sources by means of different Green's functions. The expression obtained for the number of level intersections by the field R(σ) is sufficient to solve a number of problems of statistical geometry in non-Gaussian fields of this class.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 133–139, June, 1977
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Shtremel', M.A., Mel'nichenko, A.S. Non-Gaussian random fields of independent sources in a discrete lattice. Soviet Physics Journal 20, 806–811 (1977). https://doi.org/10.1007/BF00892771
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DOI: https://doi.org/10.1007/BF00892771