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Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

  • David Alonso-Gutiérrez
  • Jesús Bastero

Part of the Lecture Notes in Mathematics book series (LNM, volume 2131)

Table of contents

  1. Front Matter
    Pages i-x
  2. David Alonso-Gutiérrez, Jesús Bastero
    Pages 1-64
  3. David Alonso-Gutiérrez, Jesús Bastero
    Pages 65-101
  4. David Alonso-Gutiérrez, Jesús Bastero
    Pages 103-135
  5. Back Matter
    Pages 137-150

About this book

Introduction

Focusing on two central conjectures from the field of Asymptotic Geometric Analysis, the Kannan-Lovász-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 topics treated. Employing a style 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, allowing readers to quickly access the core of these conjectures.

In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan’s work on the connection between the thin-shell width and the KLS conjecture.

Keywords

46Bxx,52Axx,60-XX,28Axx. Convex bodies Isoperimetric inequalities Poincaré's inequalities for log-concave probabilities Spectral gap estimates Variance conjecture

Authors and affiliations

  • David Alonso-Gutiérrez
    • 1
  • Jesús Bastero
    • 2
  1. 1.Departament de Matemàtiques and IMACUniversitat Jaume ICastelló de la PlanaSpain
  2. 2.Departamento de Matemáticas and IMACUniversidad de ZaragozaZaragozaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-13263-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-13262-4
  • Online ISBN 978-3-319-13263-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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