Stochastic localization + Stieltjes barrier = tight bound for log-Sobolev

@inproceedings{Lee2017StochasticL,
  title={Stochastic localization + Stieltjes barrier = tight bound for log-Sobolev},
  author={Yin Tat Lee and Santosh S. Vempala},
  booktitle={STOC},
  year={2017}
}
Logarithmic Sobolev inequalities are a powerful way to estimate the rate of convergence of Markov chains and to derive concentration inequalities on distributions. We prove that the log-Sobolev constant of any isotropic logconcave density in <i>R</i><sup><i>n</i></sup> with support of diameter <i>D</i> is Ω(1/<i>D</i>), resolving a question posed by Frieze and Kannan in 1997. This is asymptotically the best possible estimate and improves on the previous bound of Ω(1/<i>D</i><sup>2</sup>) by… CONTINUE READING
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