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Approaching the Kannan-Lovasz-Simono...

Alonso-Gutierrez, David.

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Approaching the Kannan-Lovasz-Simonovits and variance conjectures

Record Type:	Electronic resources : Monograph/item
Title/Author:	Approaching the Kannan-Lovasz-Simonovits and variance conjectures/ by David Alonso-Gutierrez, Jesus Bastero.
Author:	Alonso-Gutierrez, David.
other author:	Bastero, Jesus.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	x, 148 p. :ill., digital ;24 cm.
[NT 15003449]:	The Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index.
Contained By:	Springer eBooks
Subject:	Geometric analysis. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-13263-1
ISBN:	9783319132631 (electronic bk.)

Approaching the Kannan-Lovasz-Simonovits and variance conjectures
Alonso-Gutierrez, David.

Approaching the Kannan-Lovasz-Simonovits and variance conjectures[electronic resource] /by David Alonso-Gutierrez, Jesus Bastero. - Cham :Springer International Publishing :2015. - x, 148 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21310075-8434 ;. - Lecture notes in mathematics ;2046..

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

Focusing on two central conjectures from the field 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 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 Guedon-Milman, and an approach to Eldan’s work on the connection between the thin-shell width and the KLS conjecture.

ISBN: 9783319132631 (electronic bk.)

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

1439441
Geometric analysis.

LC Class. No.: QA360

Dewey Class. No.: 515.1

Approaching the Kannan-Lovasz-Simonovits and variance conjectures
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245 1 0 $a Approaching the Kannan-Lovasz-Simonovits and variance conjectures $h [electronic resource] / $c by David Alonso-Gutierrez, Jesus Bastero.
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505 0 $a The Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index.
520 $a Focusing on two central conjectures from the field 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 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 Guedon-Milman, and an approach to Eldan’s work on the connection between the thin-shell width and the KLS conjecture.
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