A note on Talagrand’s transportation inequality and logarithmic Sobolev inequality
By Patrick Cattiaux, Arnaud Guillin, Liming Wu. 2008
81 citations recorded by the source corpus.
We give by simple arguments sufficient conditions, so called Lyapunov conditions, for Talagrand’s transportation information inequality and for the logarithmic Sobolev inequality. Those sufficient conditions work even in the case where the Bakry–Emery curvature is not lower bounded. Several new examples are provided.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/8d5684d987134fdaffdb381a25751de32a9af4e2
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
- Arnaud Guillin
- Raphael Zimmer
- Andreas Eberle
- Maxim Raginsky
- Alexander Rakhlin
- Matus Telgarsky
- Nathael Gozlan
- Patrick Cattiaux
Citations in the corpus
- Quantitative Harris-type theorems for diffusions and McKean–Vlasov processes (2016, background): “Assumptions linking curvature and the Lyapunov function already appeared in [13] to prove a logarithmic Sobolev inequality in the reversible setting in the case where the curvature may explode (polynomially).”
- Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis (2017, methodology): “This modification is closely related to the Entropy-SGDmethod, recently proposed by Chaudhari et al. (2016). Observe that the modified Gibbs measures π̃z(dw) ∝ e−βF̃z(w) are convolutions of a Gaussian measure and a compactly supported probability measure.”