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Approaching the Kannan-Lovász-Simonovits and variance conjectures [electronic resource] / David Alonso-Gutiérrez, Jesús Bastero.

9783319132631 electronic book
3319132636 electronic book
9783319132624

Cham : Springer, 2015.

©2015

English

1 online resource (x, 148 pages).

10.1007/978-3-319-13263-1 doi

QA360

515/.1

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed January 28, 2015).

Lecture notes in mathematics (Springer-Verlag) ; 2131.

Print version: 9783319132624

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