An Example of Application of Discrete Hardy's Inequalities

L. Miclo

1999, v.5, Issue 3, 319-330


After having given a short proof of weighted Hardy's inequalities on N, adapted from the continuous case, we show how to use them to evaluate, up to a universal factor, spectral gaps and logarithmic Sobolev constants of birth and death processes on Z. We illustrate this method by giving an example of such calculation.

Keywords: birth and death Markov processes,spectral gaps,weighted Hardy's inequalities on discrete intervals


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