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AuthorSznitman, Alain-Sol. author
TitleBrownian Motion, Obstacles and Random Media [electronic resource] / by Alain-Sol Sznitman
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
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Descript XVI, 357 p. 16 illus. online resource


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


1. The Feynman-Kac Formula and Semigroups -- 2. Some Potential Theory -- 3. Some Principal Eigenvalue Estimates -- 4. The Method of Enlargement of Obstacles -- 5. Lyapunov Exponents -- 6. Quenched Path Measure and Pinning Effect -- 7. Overview, further Results and Problems -- References

Mathematics Partial differential equations Probabilities Physics Mathematics Probability Theory and Stochastic Processes Partial Differential Equations Theoretical Mathematical and Computational Physics


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