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Modified log-Sobolev inequalities for strongly log-concave distributions
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math.PRcs.DSmath.CO
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bounddistributionslog-concavelog-sobolevmodifiedstronglyapplicationsbases-exchange
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abstract
We show that the modified log-Sobolev constant for a natural Markov chain which converges to an $r$-homogeneous strongly log-concave distribution is at least $1/r$. Applications include a sharp mixing time bound for the bases-exchange walk for matroids, and a concentration bound for Lipschitz functions over these distributions.
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