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Relating the Conjectures

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Approaching the Kannan-Lovász-Simonovits and Variance Conjectures

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2131))

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Abstract

In this chapter the results due to Eldan-Klartag and Ball-Nguyen showing how the KLS conjecture and the variance conjecture are related to slicing problem 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 logarithmic factor, as Eldan proved.

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Authors and Affiliations

  1. Departament de Matemàtiques and IMAC, Universitat Jaume I, Castelló de la Plana, Spain

    David Alonso-Gutiérrez

  2. Departamento de Matemáticas and IUMA, Universidad de Zaragoza, Zaragoza, Spain

    Jesús Bastero

Authors
  1. David Alonso-Gutiérrez
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  2. Jesús Bastero
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Alonso-Gutiérrez, D., Bastero, J. (2015). Relating the Conjectures. In: Approaching the Kannan-Lovász-Simonovits and Variance Conjectures. Lecture Notes in Mathematics, vol 2131. Springer, Cham. https://doi.org/10.1007/978-3-319-13263-1_3

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