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Limit Theorems For Associated Random Fields And Related Systems
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This volume is devoted to the study of asymptotic properties of wide classes of stochastic models arising in mathematical statistics, percolation theory, statistical physics and reliability theory. Attention is paid not only to positive and negative associations introduced in the pioneering papers by Harris, Lehmann, Esary, Proschan, Walkup, Fortuin, Kasteleyn and Ginibre, but also to new and more general dependence conditions. Naturally, this scope comprises families of independent real-valued random variables. A variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models are provided.For such random systems, it is worthwhile to establish principal limit theorems of the modern probability theory (central limit theorem for random fields, weak and strong invariance principles, functional law of the iterated logarithm etc.) and discuss their applications. Parts of the text are based on lectures delivered by the authors at the Moscow State University. For the sake of readers' convenience, some auxiliary results are also included, some of them in the Appendix (e.g. the classical Hoeffding lemma, basic electric current theory etc.).
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