Displacement convexity of entropy and related inequalities on graphs
By Nathael Gozlan, Cyril Roberto, Paul-Marie Samson, Prasad Tetali. Probability theory and related fields, 2012
53 citations recorded by the source corpus.
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 Prékopa-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.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/5ea74e0bdc3e82799cc3982190ed60c1344872d4
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Nathael Gozlan
- Cyril Roberto
- Prasad Tetali
- Paul-Marie Samson
- Emanuel Milman
- Gady Kozma
- Peter Ralli
- Bo'az Klartag
Citations in the corpus
- Discrete Curvature and Abelian Groups (2015, background): “_is notion as a possible deûnition of Ricci curvature in Markov chainswas in fact considered and discussed in [32] in 1999, but seems to have largely been neglected ever since.”
- Kantorovich duality for general transport costs and applications (2014, methodology): “8) was already put to use in [30], in connection with displacement convexity of the relative entropy functional on graphs.”