Geometric & Functional Analysis GAFA

, Volume 3, Issue 3, pp 295–314

Isoperimetry, logarithmic sobolev inequalities on the discrete cube, and margulis' graph connectivity theorem

  • M. Talagrand
Article

DOI: 10.1007/BF01895691

Cite this article as:
Talagrand, M. Geometric and Functional Analysis (1993) 3: 295. doi:10.1007/BF01895691

Abstract

We prove that the suitably defined surface area of a subsetA of the cube {0,1}n is bounded below by a certain explicit function of the size ofA. We establish a family of logarithmic Sobolev inequalities on the cube related to this isoperimetric result. We also give a quantitative version of Margulis' graph connectivity theorem.

Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • M. Talagrand
    • 1
    • 2
  1. 1.Equipe d'Analyse-Tour 48 U.A. au C.N.R.S. no. 745Université Paris VIParis Cedex 05France
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA