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5 produkter
5 produkter
Del 1464 - Lecture Notes in Mathematics
Ecole d'Ete de Probabilites de Saint-Flour XIX - 1989
Häftad, Engelska, 1991
488 kr
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541 kr
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This book is aimed at graduate students and researchers. It provides an account for the non-specialist of the circle of ideas, results and techniques, which grew out in the study of Brownian motion and random obstacles. This subject has a rich phenomenology which exhibits certain paradigms, emblematic of the theory of random media. It also brings into play diverse mathematical techniques such as stochastic processes, functional analysis, potential theory, first passage percolation. In a first part, the book presents, in a concrete manner, background material related to the Feynman-Kac formula, potential theory, and eigenvalue estimates. In a second part, it discusses recent developments including the method of enlargement of obstacles, Lyapunov coefficients, and the pinning effect. The book also includes an overview of known results and connections with other areas of random media.
540 kr
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The principal purpose of this book is to provide an account of the circle of ideas, results and techniques, which emerged roughly over the last ten years in the study of Brownian motion and random obstacles. The accumulation of results in many separate sources eventually made it impractical, if not impossible, for the nonspecialist to gain access to the developments of the subject. This book is an attempt to remedy this situation. Part of the thrill of the investigation of Brownian motion and random obsta cles certainly stems from its many connections with various areas of math ematics, but also from the formal and mysterious physical heuristics which relate to it. In particular the loose concept of pockets of low local eigenval ues plays an important role in the study of Brownian motion and random obstacles, and also represents a paradigm which has natural resonances with several other areas of random media. This last feature has increasingly be come clear over the last few years.
380 kr
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Contents: Durrett, Rick: Ten lectures on particle systems.- Liggett, T.M.: The stochastic evolution of infinite systems of interacting particles.- Spitzer, Frank L.:Introduction aux processus de Markov à paramètre dans Zʋ
327 kr
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The field of random media gathers a variety of models generally originating from physical sciences, where certain materials or substances have defects or inhomogeneities. This feature can be taken into account by letting the medium be random. Randomness in the medium turns out to cause very unexpected effects, especially in the large-scale behaviour of some of these models. What in the beginning was often deemed to be a simple toy-model ended up as a major mathematical challenge. After more than 25 years of intensive research in this field, certain new paradigms and some general methods have emerged, and the surprising results on the asymptotic behaviour of individual models are now better understood in more general frameworks. This monograph grew out of the DMV lectures on random media held by the authors at the Mathematical Research Institute in Oberwolfach in November 1999 and gives an account of some of the developments in the field, especially in the area of random motions in random media and of mean-field spin glasses. Postgraduates and researchers in probability theory and mathematical physics should find it a valuable resource.