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Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Approaching the Kannan-Lovász-Simonovits and Variance Conjectures/ by David Alonso-Gutiérrez, Jesús Bastero.
Author:	Alonso-Gutiérrez, David.
other author:	Bastero, Jesús.
Description:	X, 148 p.online resource. :
Contained By:	Springer Nature eBook
Subject:	Functional analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-13263-1
ISBN:	9783319132631

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures
Alonso-Gutiérrez, David.

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures[electronic resource] /by David Alonso-Gutiérrez, Jesús Bastero. - 1st ed. 2015. - X, 148 p.online resource. - Lecture Notes in Mathematics,21310075-8434 ;. - Lecture Notes in Mathematics,2144.

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

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.

ISBN: 9783319132631

Standard No.: 10.1007/978-3-319-13263-1doiSubjects--Topical Terms:

527706
Functional analysis.

LC Class. No.: QA319-329.9

Dewey Class. No.: 515.7

Approaching the Kannan-Lovász-Simonovits and Variance Conjectures
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