Approaching the Kannan-Lovasz-Simonovits and Variance Conjectures PDF ePub eBook

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Approaching the Kannan-Lovasz-Simonovits and Variance Conjectures free pdf Focusing on two central conjectures 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 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 Guedon-Milman and an approach to Eldan's work on the connection between the thin-shell width and the KLS conjecture are detailed.

About David Alonso-Gutierrez

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Details Book

Author : David Alonso-Gutierrez
Publisher : Springer International Publishing AG
Data Published : 20 January 2015
ISBN : 3319132628
EAN : 9783319132624
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 148 pages
Age + : 15 years
Language : English
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  • Approaching the Kannan-Lovasz-Simonovits and Variance Conjectures free pdfApproaching the Kannan-Lovasz-Simonovits and Variance Conjectures

    . Focusing on two central conjectures of Asymptotic Geometric Analysis, the Kannan-Lovasz-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an a