Overview
- The 2007 monograph has been very well received, but does not make for easy reading. The current notes, while not as exhaustive, are much more readable. As such, they provide a comparatively easy entry into a difficult, but important, area of research This is the main contribution of these notes...
- There are no real competitors to these notes, beyond our 2007 book. Recent reprintings of Adler's `Geometry of Random Fields' (1980) by SIAM and Vanmarke's `Random Fields: Analysis and Synthesis" (1983) are not competitors. Both are terribly out of date.
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2019)
Part of the book sub series: École d'Été de Probabilités de Saint-Flour (LNMECOLE)
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Table of contents (6 chapters)
Keywords
About this book
Reviews
From the reviews:
“These little lecture notes are a rare delight. The authors succeed in an impressive manner to combine a writing style that focuses on the main ideas and intuitions while still stating all the results in full mathematical rigor. They take the reader on an exciting journey through the theories of Gaussian processes and differential topology and geometry and then show how fascinating mathematics arises when combining these fields not to speak about the wide range of applications.” (H. M. Mai, Zentralblatt MATH, Vol. 1230, 2012)
“This concise book is written for graduate students as well as researchers who want to learn the state of the art of geometry of smooth Gaussian (and Gaussian-related) random fields and their significant applications. … The authors have done an excellent job in showing not only the mathematical beauty and the essence of the ‘Gaussian Kinematic Formulae’, but also their powerful applicability. The book is very interesting to read.” (Yimin Xiao, Mathematical Reviews, Issue 2012 h)
Authors and Affiliations
Bibliographic Information
Book Title: Topological Complexity of Smooth Random Functions
Book Subtitle: École d'Été de Probabilités de Saint-Flour XXXIX-2009
Authors: Robert J. Adler, Jonathan E. Taylor
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-642-19580-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Softcover ISBN: 978-3-642-19579-2Published: 18 May 2011
eBook ISBN: 978-3-642-19580-8Published: 16 May 2011
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: VIII, 122
Number of Illustrations: 6 b/w illustrations, 9 illustrations in colour
Topics: Geometry, Statistical Theory and Methods