R J Adler

(Author)

Random Fields and GeometryHardcover, 12 June 2007

Random Fields and Geometry
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Part of Series
Springer Monographs in Mathematics
Print Length
454 pages
Language
English
Publisher
Springer
Date Published
12 Jun 2007
ISBN-10
0387481125
ISBN-13
9780387481128

Description

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined.

The three parts to the monograph are quite distinct. Part I presents a user-friendly yet comprehensive background to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness, entropy and majorizing measures, Borell and Slepian inequalities. Part II gives a quick review of geometry, both integral and Riemannian, to provide the reader with the material needed for Part III, as well as providing some new results and new proofs of known results along the way. Topics such as Crofton formulae, curvature measures for stratified manifolds, critical point theory, and tube formulae are covered. In fact, this is the only concise, self-contained treatment of all of the above topics, which are necessary for the study of random fields. The new approach in Part III is devoted to the geometry of excursion sets of random fields and the related Euler characteristic approach to extremal probabilities.

Product Details

Authors:
R J AdlerJonathan E Taylor
Book Format:
Hardcover
Country of Origin:
US
Date Published:
12 June 2007
Dimensions:
23.55 x 16.15 x 2.64 cm
ISBN-10:
0387481125
ISBN-13:
9780387481128
Language:
English
Location:
New York, NY
Pages:
454
Publisher:
Weight:
757.5 gm

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