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Poincaré inequality and the Lp convergence of semi-groups
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Patrick Cattiaux, Institut de Mathématiques de Toulouse
Arnaud Guillin, Université Blaise Pascal
Cyril Roberto, Universités de Paris Est Marne la Vallée et de Paris 12-Val-de-Marne
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Abstract
We prove that for symmetric Markov processes of diffusion type admitting a ``carré du champ'', the Poincaré inequality is equivalent to the exponential convergence of the associated semi-group in one (resp. all) Lp(μ) spaces for 1<p<+∞. We also give the optimal rate of convergence. Part of these results extends to the stationary, not necessarily symmetric situation
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Full text: PDF
Pages: 270-280
Published on: July 4, 2010
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Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X |
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