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9780898716931 Academic Inspection Copy

The Geometry of Random Fields

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Originally published in 1981, The Geometry of Random Fields remains an important text for its coverage and exposition of the theory of both smooth and non-smooth 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. The Geometry of Random Fields is essential reading for 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.
Robert Adler holds the Louis and Samuel Seiden Academic Chair at the Technion - Israel Institute of Technology in Haifa where he has a joint appointment between the Faculty of Industrial Engineering and Management and the Faculty of Electrical Engineering. He holds degrees from Sydney University (BSc), the Australian National University (MSc) and the University of New South Wales (PhD).
Preface to the Classics edition; Preface; Corrections and comments; 1. Random fields and excursion sets; 2. Homogeneous fields and their spectra; 3. Sample function regularity; 4. Geometry and excursion characteristics; 5. Some expectations; 6. Local maxima and high-level excursions; 7. Some non-Gaussian fields; 8. Sample function erraticism and Hausdorff dimension; Appendix. The Markov property for Gaussian fields; References; Author index; Subject index.
An important exposition of the geometric properties of sets generated by random fields.
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