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Author Alonso-Gutierrez, David, author.

Title Approaching the Kannan-Lovász-Simonovits and variance conjectures / David Alonso-Gutiérrez, Jesús Bastero.

Published Cham : Springer, 2015.


Location Call No. Status
Physical description 1 online resource (x, 148 pages).
Series Lecture notes in mathematics, 0075-8434 ; 2131
Lecture notes in mathematics (Springer-Verlag) ; 2131. 0075-8434
Springer English/International eBooks 2015 - Full Set
Bibliography Includes bibliographical references and index.
Contents The Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index.
Summary 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.
Other author Bastero, J. (Jesús), 1950- author.
SpringerLink issuing body.
Subject Geometric analysis.
Functional analysis.
Electronic books.
Electronic books.
ISBN 9783319132631
3319132628 (print)
9783319132624 (print)
Standard Number 10.1007/978-3-319-13263-1