Titlebook: Probability and Phase Transition; Geoffrey Grimmett Book 1994 Springer Science+Business Media Dordrecht 1994 Markov chain.Probability theo

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Gregory F. Lawlereful to the readers for their kind feedbacks, many of which are included in this edition. I hope this English publication attracts readers in wider areas, and evokes valuable feedbacks furthermore. In the months after the Japanese publication, researches on the compl- valued neural networks have kep

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R. Pemantle,Y. Peresd by Saiensu-sha, Japan, in March 2005, has fortunately acquired a favorable reputation. I am grateful to the readers for their kind feedbacks, many of which are included in this edition. I hope this English publication attracts readers in wider areas, and evokes valuable feedbacks furthermore. In t

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Droplet Condensation in the Ising Model: Moderate Deviations Point of View,el. The parameter which drives the condensation is the amount of the condensing phase, and the critical value of it, which turns the condensation on, is found to be of the order of IVNI(v.)/v, where ∣VN∣ is the volume of the system. The corresponding behaviour of large and moderate deviations is stu

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