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＜電子ブック＞
Approaching the Kannan-Lovász-Simonovits and Variance Conjectures / by David Alonso-Gutiérrez, Jesús Bastero
(Lecture Notes in Mathematics. ISSN:16179692 ; 2131)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	X, 148 p : online resource
著者標目	*Alonso-Gutiérrez, David author Bastero, Jesús author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Probabilities FREE:Functional Analysis FREE:Convex and Discrete Geometry FREE:Probability Theory
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-13263-1

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