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" Ten Lectures on Random Media "
by Erwin Bolthausen, Alain-Sol Sznitman.
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BL
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768068
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b588054
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by Erwin Bolthausen, Alain-Sol Sznitman.
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Ten Lectures on Random Media\ by Erwin Bolthausen, Alain-Sol Sznitman.
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| Publication Statement
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Basel : Birkhäuser Basel : Imprint : Birkhäuser, 2002
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DMV Seminar, 32.
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(vi, 116 pages)
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3034881592
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: 9783034881593
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| Contents
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One: Lectures on Random Motions in Random Media --; A 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 Environment --; 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 Equation --; References.
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| Abstract
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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.
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Mathematics.
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QA274.B947 2002
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Alain-Sol Sznitman
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Erwin Bolthausen
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