Approaching the Kannan-Lovász-Simonovits and Variance Conjectures [electronic resource] / by David Alonso-Gutiérrez, Jesús Bastero.

By: Alonso-Gutiérrez, David [author.]Contributor(s): Bastero, Jesús [author.] | SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Mathematics ; 2131Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Edition: 1st ed. 2015Description: X, 148 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319132631Subject(s): Functional analysis | Convex geometry | Discrete geometry | Probabilities | Functional Analysis | Convex and Discrete Geometry | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 515.7 LOC classification: QA319-329.9Online resources: Click here to access online
Contents:
The Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index.
In: Springer Nature eBookSummary: 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.
Item type: E-BOOKS
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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.

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