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Random Fields and Geometry

Random Fields and Geometry by R.J. Adler
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This self-contained monograph focuses on recent important developments in the study of random fields, stochastic processes defined over high dimensional parameter spaces. While it replaces Adler's 1981 classic, "The Geometry of Random Fields", this is not an update, but a completely new work with a completely new way of handling both the geometry and the probability that are its central themes.There are three quite distinct parts to the monograph. Part I provides a comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorising measures, Borell and Slepian inequalities. The treatment is didactic and user-friendly. Part II is about Geometry, both integral and Riemannian, and the material included here is what is needed for the over-riding probabilistic theme of the book. It contains a quick review of both these geometric settings, followed by carefully presented introductions to topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory and tube formulae.
Springer; January 2009
464 pages; ISBN 9780387481166
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Title: Random Fields and Geometry
Author: R.J. Adler; Jonathan Taylor
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