Titlebook: Entropy, Large Deviations, and Statistical Mechanics; Richard S. Ellis Book 1985 Springer-Verlag New York Inc. 1985 Large.Maxwell-Boltzman

Foreknowledge

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Convex Functions and the Legendre-Fenchel Transforming theme. Suppose that . is a probability measure on ℝ. such that.is finite for all . in ℝ.. The function .(.), called the free energy function of ., is a convex function on ℝ. [Example VII.1.2]. The Legendre-Fenchel transform of .(.) is given by

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0072-7830 many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law

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Das wechselhafte Leben der Sterneilibrium statistical mechanics is to explain phase transitions in terms of the probability distributions on configuration space which describe the microscopic behavior of physical systems. The simplest systems for which this is possible are ferromagnetic models on a lattice. The present chapter introduces these models.

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https://doi.org/10.1007/1-84628-129-6ctions VII.2–VII.4] and the level-1 large deviation property will be derived as a corollary [Section VII.5]. The results on exponential convergence of random vectors stated in Theorem 1I.6.3 will be proved in Section VII.6.

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