Hamming cube and martingales |
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| Authors: | Paata Ivanisvili Fedor Nazarov Alexander Volberg |
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| Affiliation: | 1. Kent State University, OH 44240, USA;2. MSRI, USA;3. Princeton University, USA;4. University of California, Irvine, USA;5. Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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| Abstract: | In the present paper, we show that a correctly chosen Legendre transform of the Bellman functions of martingale problems give us the right tool to prove isoperimetric inequalities on Hamming cube independent of the dimension. We illustrate the power of this “dual function approach” by proving certain Poincaré inequalities on Hamming cube and by improving a particular inequality of Beckner on the Hamming cube. |
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