The Logarithmic Sobolev Constant of The Lamplighter

Abstract : We give estimates on the logarithmic Sobolev constant of some finite lamplighter graphs in terms of the spectral gap of the underlying base. Also, we give examples of application.
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Evgeny Abakumov, Anne Beaulieu, François Blanchard, Matthieu Fradelizi, Nathaël Gozlan, et al.. The Logarithmic Sobolev Constant of The Lamplighter. Journal of Mathematical Analysis and Applications, Elsevier, 2013, 399, pp.576-585. ⟨10.1016/j.jmaa.2012.10.002⟩. ⟨hal-00533572⟩

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