Adler R.J. The Geometry of Random Fields

Philadelphia: Society for Industrial and Applied Mathematics, 2010. — 295 p. — (Classics in Applied Mathematics 62). — ISBN: 0898716934, 9780898716931Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and nonsmooth random fields
closed form expressions for various geometric characteristics of the excursion sets of smooth, stationary, Gaussian random fields over N-dimensional rectangles
descriptions of the local behavior of random fields in the neighborhoods of high MAXIMA
and a treatment of the Markov property for Gaussian fields.
Audience: The core audience of the book is researchers in probability and statistics, with no prior knowledge of geometry required. Since the book was originally published it has become a standard reference in areas of physical oceanography, cosmology, and neuroimaging. It is written at a level accessible to nonspecialists, including advanced undergraduates and early graduate students.Preface to the Classics EditionCorrections and Comments
Random Fields and Excursion Sets
Homogeneous Fields and Their Spectra
Sample Function Regularity
Geometry and Excursion Characteristics
Some Expectations
Local MAXIMA and High-Level Excursions
Some Non-Gaussian Fields
Sample Function Erraticism and Hausdorff Dimension
Appendix: The Markov Property for Gaussian FieldsAuthor Index
Subject Index.