Logo - springer
Slogan - springer

Mathematics - Geometry & Topology | Topological Complexity of Smooth Random Functions - École d'Été de Probabilités de Saint-Flour

Topological Complexity of Smooth Random Functions

École d'Été de Probabilités de Saint-Flour XXXIX-2009

Adler, Robert, Taylor, Jonathan E.

2011, VIII, 122 p. 15 illus., 9 illus. in color.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-642-19580-8

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-642-19579-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • 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 Both are terribly out of date.
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.

Content Level » Research

Keywords » 60-02, 60G15, 55N35, 60Gxx, 60G60, 53Cxx, 62H35, 60G55, 53C65 - Differential topology - Gaussian extrema - Gaussian processes - Random fields - Stochastic geometry

Related subjects » Geometry & Topology - Statistical Theory and Methods

Table of contents / Preface / Sample pages 

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Geometry.