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001 978-3-319-13263-1
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020 _a9783319132631
_9978-3-319-13263-1
024 7 _a10.1007/978-3-319-13263-1
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aAlonso-Gutiérrez, David.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aApproaching the Kannan-Lovász-Simonovits and Variance Conjectures
_h[electronic resource] /
_cby David Alonso-Gutiérrez, Jesús Bastero.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aX, 148 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2131
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 _aDiscrete groups.
650 0 _aDistribution (Probability theory.
650 1 4 _aFunctional Analysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12066
650 2 4 _aConvex and Discrete Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21014
650 2 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
700 1 _aBastero, Jesús.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319132648
776 0 8 _iPrinted edition:
_z9783319132624
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2131
856 4 0 _uhttps://doi.org/10.1007/978-3-319-13263-1
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c12168
_d12168