For reversible mean-field dynamics on finite state spaces, a positive entropic Ricci curvature bound implies modified logarithmic Sobolev, Talagrand transport-entropy and exponential entropy decay inequalities.
A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov processes. In this setting, the large deviation rate function of the stationary measures of the Markov processes, plays the role of entropy. We define an entropy-information inequality (EII) that generalizes the (MLSI) and is equivalent to exponential decay of the rate function along the flow, and define an entropy-convexity inequality (ECI) that serves as an analogue of a lower bound on the Ricci-curvature in this setting.
fields
math.PR 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces
For reversible mean-field dynamics on finite state spaces, a positive entropic Ricci curvature bound implies modified logarithmic Sobolev, Talagrand transport-entropy and exponential entropy decay inequalities.