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Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

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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.

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Detail Information

Series Title

Lecture Notes in Mathematics

Call Number

515.7 ALO a

Publisher

Cham, Switzerland : Springer Cham., 2015

Collation

X, 148

Language

English

ISBN/ISSN

978-3-319-13263-1

Classification

515.7

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Functional Analysis
Convex and Discrete Geometry

Specific Detail Info

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Statement of Responsibility

David Alonso-Gutiérrez, Jesús Bastero

Other Information

Cataloger

umi

Source

https://link.springer.com/book/10.1007/978-3-319-13263-1

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maya

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