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



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Autore: Alonso-Gutiérrez, David Visualizza persona
Titolo: Approaching the Kannan-Lovász-Simonovits and variance conjectures / David Alonso-Gutiérrez, Jesús Bastero Visualizza cluster
Pubblicazione: Cham : Springer, 2015
Descrizione fisica: x, 148 p. ; 24 cm
Disciplina: 515.1
Soggetto topico: Functional analysis
Geometric analysis
Classificazione: AMS 46-02
AMS 28A
AMS 46B25
AMS 52A22
AMS 60D05
Altri autori: Bastero, Jesúsauthor  
Nota di bibliografia: Includes bibliographical references and index
Nota di contenuto: The conjectures ; Main examples ; Relating the conjectures ; Appendix ; Index
Sommario/riassunto: 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
ISBN: 9783319132624
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: b14259746
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Serie: Lecture notes in mathematics, 0075-8434 ; 2131