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100   $a20150107d2015      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aApproaching the Kannan-Lovász-Simonovits and Variance Conjectures$b[electronic resource] /$fby David Alonso-Gutiérrez, Jesús Bastero
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (X, 148 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2131
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-319-13262-8 
327   $aThe Conjectures -- Main Examples -- Relating the Conjectures -- Appendix -- Index.
330   $aFocusing on two central conjectures from the field of Asymptotic Geometric Analysis, the Kannan-Lovász-Simonovits spectral gap conjecture and the variance conjecture, these Lecture Notes present the theory in an accessible way, so that interested readers, even those who are not experts in the field, will be able to appreciate the topics treated. Employing a style suitable for professionals with little background in analysis, geometry or probability, the work goes directly to the connection between isoperimetric-type inequalities and functional inequalities, allowing readers to quickly access the core of these conjectures. In addition, four recent and important results concerning this theory are presented. The first two are theorems attributed to Eldan-Klartag and Ball-Nguyen, which relate the variance and the KLS conjectures, respectively, to the hyperplane conjecture. The remaining two present in detail the main ideas needed to prove the best known estimate for the thin-shell width given by Guédon-Milman, and an approach to Eldan?s work on the connection between the thin-shell width and the KLS conjecture.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2131
606   $aFunctional analysis
606   $aConvex geometry 
606   $aDiscrete geometry
606   $aProbabilities
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
615  0$aFunctional analysis.
615  0$aConvex geometry .
615  0$aDiscrete geometry.
615  0$aProbabilities.
615 14$aFunctional Analysis.
615 24$aConvex and Discrete Geometry.
615 24$aProbability Theory and Stochastic Processes.
676   $a515.7
700   $aAlonso-Gutiérrez$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0716387
702   $aBastero$b Jesús$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996198828703316
996   $aApproaching the Kannan-Lovász-Simonovits and Variance Conjectures$92105502
997   $aUNISA