Between Sobolev and Poincaré

Details Between Sobolev and Poincaré Between Sobolev and Poincaré

2000-03-07

arxiv.org/abs/math/0003043v1

Mathematics

Probability

23 pages

Scientific paper

We establish a family of functional inequalities interpolating between the
classical logarithmic Sobolev and Poincar\'e inequalities. We prove that they
imply the concentration of measure phenomenon intermediate between Gaussian and
exponential. Our bounds are close to optimal.

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