Abstract
A random-medium model being the correlated distribution of points positioned in E-dimensional Euclidean space is considered. The construction of the medium starts from noncorrelated (Poisson) uniform distribution of parent particles; each of them initiates the finite Marcov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model has been obtained. The use of three-dimensional stable laws (Lévy laws) as transition probability density allows one to express the correlation functions of all orders in terms of two point ones only. Some numerical results are presented and discussed in connection with fractal structure simulation.
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