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.
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Work partially supported by the US-Israel Binational Science Foundation.
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Talagrand, M. Isoperimetry, logarithmic sobolev inequalities on the discrete cube, and margulis' graph connectivity theorem. Geometric and Functional Analysis 3, 295–314 (1993). https://doi.org/10.1007/BF01895691
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DOI: https://doi.org/10.1007/BF01895691