Isoperimetry,logarithmic sobolev inequalities on the discrete cube,and margulis' graph connectivity theorem |
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| Authors: | M Talagrand |
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| Institution: | (1) Equipe d'Analyse-Tour 48 U.A. au C.N.R.S. no. 745, Université Paris VI, 4 Pl. Jussieu, 75230 Paris Cedex 05, France;(2) Department of Mathematics, Ohio State University, 231 West 18th Avenue, 43210 Columbus, Ohio, USA |
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| 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.Work partially supported by the US-Israel Binational Science Foundation. |
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