Authors:
- Provides a rapid introduction to Asymptotic Geometric Analysis
- Presents a modern approach to two central problems in Asymptotic Geometric Analysis: The Kannan-Lovasz-Simmonovits Conjecture and the Variance (or Thin Shell) Conjecture
- Details the results and methods in as elementary a way as possible, aiming the presentation at a wide audience
- Introduces interested readers to a fascinating area of research
- Provides a useful starting point for young researchers who wish to work on these conjectures
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2131)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
About this book
Focusing on two central conjectures 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 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 Guédon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.
Reviews
“This book serves as an excellent and well-written introduction to a fascinating and active research subject. It is a must have for specialists as well as students interested in diving into this subject, but it is also suitable for mathematicians with a different focus who are interested in a taste of this theory. It can also easily be used as a basis for an advanced course.” (Ronen Eldan, Mathematical Reviews, October, 2015)
Authors and Affiliations
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Departament de Matemàtiques and IMAC, Universitat Jaume I, Castelló de la Plana, Spain
David Alonso-Gutiérrez
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Departamento de Matemáticas and IMAC, Universidad de Zaragoza, Zaragoza, Spain
Jesús Bastero
Bibliographic Information
Book Title: Approaching the Kannan-Lovász-Simonovits and Variance Conjectures
Authors: David Alonso-Gutiérrez, Jesús Bastero
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-13263-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Softcover ISBN: 978-3-319-13262-4Published: 20 January 2015
eBook ISBN: 978-3-319-13263-1Published: 07 January 2015
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 148
Topics: Functional Analysis, Convex and Discrete Geometry, Probability Theory and Stochastic Processes