Modified Logarithmic Sobolev Inequalities in Discrete Settings

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Displacement convexity of entropy and related inequalities on graphs (2012, unknown): “[7] , [10], [5], [13], [14], [46], [44].”
Strong Data Processing Inequalities and $\Phi $ -Sobolev Inequalities for Discrete Channels (2014, methodology): “…we have Applying this and Theorem IV.4, we get the following upper and lower bounds on the log-Sobolev constant ˜ ρ 1 : Unfortunately, neither of the bounds is tight, since the log-Sobolev constant in this case is known exactly: ˜ ρ 1 (cid:29) Bern ( 1 / 2 ), BSC (ε) (cid:30) = ε [26, Example 3.9].”
Kantorovich duality for general transport costs and applications (2014, background): “[52, 12]), the other terms are far from well understood.”
Correlation and Brascamp–Lieb Inequalities for Markov Semigroups (2009, background): “In the discrete case, some examples of superadditive inequalities for Fisher information were implicitly obtained in the papers [9, 18, 19].”