Approaching the Kannan-Lovász-Simonovits and variance conjectures

Bibliographic Information

Approaching the Kannan-Lovász-Simonovits and variance conjectures

David Alonso-Gutiérrez, Jesús Bastero

(Lecture notes in mathematics, 2131)

Springer, c2015

Available at  / 38 libraries

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Includes bibliographical references and index

Description and Table of Contents

Description

Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the treated topics. Offering a presentation suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, giving the interested reader rapid access to the core of these conjectures. In addition, four recent and important results in this theory are presented in a compelling way. The first two are theorems due to Eldan-Klartag and Ball-Nguyen, relating the variance and the KLS conjectures, respectively, to the hyperplane conjecture. Next, the main ideas needed prove the best known estimate for the thin-shell width given by Guedon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.

Table of Contents

The Conjectures.- Main Examples.- Relating the Conjectures.- Appendix.- Index.

by "Nielsen BookData"

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Details

  • NCID
    BB17906499
  • ISBN
    • 9783319132624
  • LCCN
    2014959425
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    x, 148 p.
  • Size
    24 cm
  • Parent Bibliography ID
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