Topological Complexity of Smooth Random Functions

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

  • Robert J. Adler
  • Jonathan E. Taylor

Part of the Lecture Notes in Mathematics book series (LNM, volume 2019)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 2019)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Robert J. Adler, Jonathan E. Taylor
    Pages 1-12
  3. Robert J. Adler, Jonathan E. Taylor
    Pages 13-35
  4. Robert J. Adler, Jonathan E. Taylor
    Pages 37-58
  5. Robert J. Adler, Jonathan E. Taylor
    Pages 59-85
  6. Robert J. Adler, Jonathan E. Taylor
    Pages 87-106
  7. Robert J. Adler, Jonathan E. Taylor
    Pages 107-114
  8. Back Matter
    Pages 115-122

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Robert J. Adler
    • 1
  • Jonathan E. Taylor
    • 2
  1. 1.Fac. Industrial Engineering &, ManagementTechnion -Israel Institute of TechnologyTechnion City, HaifaIsrael
  2. 2.Dept. StatisticsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-19580-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-19579-2
  • Online ISBN 978-3-642-19580-8
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book