Ten lectures on random media隨機(jī)媒介講座

內(nèi)容概要

The field of random media has been the object of intensive activity over the last twenty-five years. It 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 behavior 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 twenty years of intensive research in this field, certain new paradigms and some general methods have emerged, and the surprising results on the asymptotic behavior 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 tries to give 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. It will be a valuable resource for postgraduates and researchers in probability theory and mathematical physics.

書籍目錄

ContentsPART ONE: Lectures on Random Motions in Random MediaForewordA Brief Introduction　Lecture 1: The Environment Viewed from the Particle　Lecture 2: Central Limit Theorem for Random Walks in Random Environment with Null Drift　Lecture 3: Long Time Survival among Random Traps　Lecture 4: Multi-dimensional Random Walks in Random Environment　Lecture 5: More on Random Walks in Random EnvironmentPART TWO: Lectures on Spin Glasses　Lecture 6: On the Sherrington-Kirkpatrick Model of Spin Glasses　Lecture 7: The Sherrington-Kirkpatrick Model: High Temperature and Nonzero Magnetic Field　Lecture 8: The Random Energy Model　Lecture 9: The Generalized Random Energy Model and Induced Clusterings　Lecture 10: Markovian Clustering, Reshuffling, and a Self-consistency EquationReferencesIndex

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