Probability theory and applications
著者
書誌事項
Probability theory and applications
（IAS/Park City mathematics series / [Dan Freed, series editor], v. 6）
American Mathematical Society , Institute for Advanced Study, c1999
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注記
"Lecture notes from the Graduate Summer School Program on Probability Theory, held in Princeton, NJ, on June 23-July 13, 1996" -- T.p. verso
Includes bibliographical references
内容説明・目次
内容説明
This volume, with contributions by leading experts in the field, is a collection of lecture notes of the six mini courses given at the IAS/Park City Summer Mathematics Institute. It introduces advanced graduates and researchers in probability theory to several of the currently active research areas in the field. Each course is self-contained with references and contains basic materials and recent results. Topics include interacting particle systems, percolation theory, analysis on path and loop spaces, and mathematical finance. The volume gives a balanced overview of the current status of probability theory. An extensive bibliography for further study and research is included. This unique collection presents several important areas of current research and a valuable survey reflecting the diversity of the field.
目次
Introduction Stochastic spatial models: Introduction The voter model Coalescing random walks Voter model with mutation The block construction Long range limits Rapid stirring limits Bibliography Independent and dependent percolation: Preface The basics of percolation Rescaling and finite-size scaling in percolation Critical exponent inequalities Two fundamental questions Finite-size scaling and the incipient infinite cluster The BK(R) inequality The Potts model and the random cluster model Bibliography Hydrodynamical scaling limits of simple exclusion models: Introduction The simple exclusion model Proof of Theorem 1.4 Local ergodicity Two-block estimate Relative entropy The Green-Kubo formula and asymmetric simple exclusion processes Some open problems Bibliography An introduction to analysis on path space: Introduction Gaussian measures on a Hilbert space Rolling on About $\mathcal {W}_M$ A few facts, and something else Bibliography Analysis on path and loop spaces: Introduction Euclidean Brownian motion Gradient operator Ornstein-Uhlenbeck operator Brownian motion on manifolds Gradient formulas Integration by parts Logarithmic Sobolev inequalities Bibliographical comments Bibliography An introduction to option pricing and the mathematical theory of risk: Introduction An introduction to option pricing and the mathematical theory of risk Bibliography.
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