, Volume 3, Issue 3, pp 295-314

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

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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.