Coupling, spectral gap and related topics (Ⅲ) |
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摘 要: |
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收稿时间: | 1997-04-04 |
Coupling, spectral gap and related topics (Ⅲ) |
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Institution: | CHEN Mufa
Department of Mathematics, Beijing Normal University, Beijing 100875, China |
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Abstract: | THIS is the last one of a series of three papers. Here, we discuss six topics related to the spectral gap: the gradient estimate, the heat kernel and Harnack inequality, the logarithmic Sobolev inequality, the convergence in total variation, the algebraic convergence and the infinite-dimensional case. The perturbation of spectral gap and the logarithmic Sobolev constant under a linear transform is given (Theorem 5). A new proof for computing the logarithmic Sobolev constant in a basic case is also presented (Theorem 7). |
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Keywords: | diffusions manifold Markov chains spectral gap couplings |
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