Titlebook: Approaching the Kannan-Lovász-Simonovits and Variance Conjectures; David Alonso-Gutiérrez,Jesús Bastero Book 2015 Springer International P

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0075-8434 respectively, to the hyperplane conjecture. Next, the main ideas needed 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 are detailed..978-3-319-13262-4978-3-319-13263-1Series ISSN 0075-8434 Series E-ISSN 1617-9692

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auxiliary

Karrierestart und ZukunftssicherungIn this second chapter the main examples known to satisfy the KLS conjecture, the square negative correlation property or the variance conjecture are provided. We also show Klartag’s results on unconditional convex bodies, which show that, up to a logarithmic factor, they verify the KLS conjecture and they verify the variance conjecture.

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https://doi.org/10.1007/978-3-8349-6538-7iginally posed in relation with some problems in theoretical computer science, and the variance conjecture, which appeared independently in relation with the central limit problem for isotropic convex bodies and is a particular case of the KLS conjecture. The relation of the KLS conjecture with Chee

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Karrierestart und Zukunftssicherungblem will be sketched. Besides, the reader can find in this chapter a sketch of the proof of the best general estimate of the thin-shell width known up to now, due to Guédon and Milman, and how the variance conjecture, despite of being weaker than the KLS conjecture, implies the latter up to a logar