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- W2949348566 abstract "We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prekopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings. To illustrate through examples, we apply our results to the complete graph and to the hypercube for which our results are optimal -- by passing to the limit, we recover the classical log-Sobolev inequality for the standard Gaussian measure with the optimal constant." @default.
- W2949348566 created "2019-06-27" @default.
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- W2949348566 date "2012-07-21" @default.
- W2949348566 modified "2023-10-01" @default.
- W2949348566 title "Displacement convexity of entropy and related inequalities on graphs" @default.
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