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008 160726s2015    sz       b    001 0 eng d
020   $a9783319132624
035   $ab14259746-39ule_inst
040   $aBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematica$beng
082 04$a515.1$223
084   $aAMS 46-02
084   $aAMS 28A
084   $aAMS 46B25
084   $aAMS 52A22
084   $aAMS 60D05
100 1 $aAlonso-Gutiérrez, David$0716387
245 10$aApproaching the Kannan-Lovász-Simonovits and variance conjectures /$cDavid Alonso-Gutiérrez, Jesús Bastero
260   $aCham :$bSpringer,$c2015
300   $ax, 148 p. ;$c24 cm
440  0$aLecture notes in mathematics,$x0075-8434 ;$v2131
504   $aIncludes bibliographical references and index
505 0 $aThe conjectures ; Main examples ; Relating the conjectures ; Appendix ; Index
520   $aFocusing on two central conjectures from the field of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the topics treated. Employing a style suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, allowing readers to quickly access the core of these conjectures. In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan?s work on the connection between the thin-shell width and the KLS conjecture
650  0$aFunctional analysis
650  0$aGeometric analysis
700 1 $aBastero, Jesús$eauthor$4http://id.loc.gov/vocabulary/relators/aut$0536463
907   $a.b14259746$b22-11-16$c26-07-16
912   $a991002954139707536
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996   $aApproaching the Kannan-Lovász-Simonovits and variance conjectures$91411158
997   $aUNISALENTO
998   $ale013$b26-07-16$cm$da  $e-$feng$gsz $h0$i0