IAS/Park City Mathematics Series 1999; 374 pp; hardcover Volume: 6 ISBN10: 0821805908 ISBN13: 9780821805909 List Price: US$65 Member Price: US$52 Order Code: PCMS/6
 This volume, with contributions by leading experts in the field, is a collection of lecture notes of the six minicourses 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 selfcontained 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. Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. Readership Advanced graduate students and researchers in probability theory; physicists and researchers in finance and economics. Table of Contents 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 finitesize scaling in percolation
 Critical exponent inequalities
 Two fundamental questions
 Finitesize 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
 Twoblock estimate
 Relative entropy
 The GreenKubo 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
 OrnsteinUhlenbeck 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
