Topological Complexity of Smooth Random Functions: École d'Été de Probabilités de Saint-Flour XXXIX-2009: 2019 (Lecture Notes in Mathematics, 2019) - Softcover

Adler, Robert; Taylor, Jonathan E.

 
9783642195792: Topological Complexity of Smooth Random Functions: École d'Été de Probabilités de Saint-Flour XXXIX-2009: 2019 (Lecture Notes in Mathematics, 2019)
Softcover
ISBN 10: 3642195792 ISBN 13: 9783642195792
Publisher: Springer, 2011

Synopsis

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

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From the Back Cover

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2011
Language
English
ISBN 10 
3642195792
ISBN 13 
9783642195792
Binding
Paperback
Number of pages
130

Other Popular Editions of the Same Title

9783642195815: Topological Complexity of Smooth Random Functions: École d'Été de Probabilités de Saint-Flour XXXIX-2009

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ISBN 10:  3642195814 ISBN 13:  9783642195815
Publisher: Springer, 2011
Softcover