An application of the Bakry-Émery criterion to infinite dimensional diffusions
An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the norms of the gradients of the functions, where the magnitude of the gradient is computed using an inner product given by the inverse Hessian matrix of the potential of the log-concave measure. Menz and Otto [Uniform logarithmic Sobolev inequalities for conservative spin systems with super-quadratic single-site potential....
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