Probability distance inequalities on Riemannian manifolds and path spaces

By Feng-Yu Wang. 2004

84 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/34371f4ddc186b080702e43261c8096d177c5b19

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In Applied Mathematics

Citations in the corpus

Poincaré inequalities and dimension free concentration of measure (2010, unknown): “Wang provides extensions of Otto and Villani’s result to Riemannian manifolds and path spaces in [40,42].”
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry (2004, background): “For other results in connection with mass transportation, see also [59,23,29].”
Quantitative Concentration Inequalities for Empirical Measures on Non-compact Spaces (2005, unknown): “Sobolev inequality [23, 6, 30], and that they imply a Poincaré, or spectral gap, inequality [23, 6].”
Exponential Contraction in Wasserstein Distances for Diffusion Semigroups with Negative Curvature (2016, background): “th domain H1,2(µ)is irreducible, according to [38] (see also [18]), the log-Sobolev inequality (3.4) holds for some constant C>0, so that (2) is proved. 18 (c) According to [25, Theorem 1.10] (see [4, 32, 20] for the case without boundary), the log-Sobolev inequality implies the Talagrand inequal”
Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion (2012, background): “The logarithmic Sobolev inequality introduced by Gross [17] plays a particular role in this theory since it implies T2(C) (see [3, 27, 32]).”
Transport Inequalities. A Survey (2010, background): “It was adapted to other situations (in particular to path spaces) by Wang in [107, 110, 109].”
A characterization of dimension free concentration in terms of transportation inequalities (2008, unknown): “Otto and Villani’s result was successfully generalized by Wang on paths spaces in [38].”
Characterization of Talagrand's like transportation-cost inequalities on the real line (2006, background): “After them, several authors studied inequality (3), possibly in a multidimensional setting, for particular choices of the cost function α (see for example [3,4,7,9,19,23]).”
Hamilton Jacobi equations on metric spaces and transport-entropy inequalities (2012, methodology): “The path space case was treated by Wang in [22].”
On quadratic transportation cost inequalities (2006, methodology): “According to Wang’s argument, under the curvature assumption, if V (x) αxp at infinity for some p > 2 then μ satisfies a log-Sobolev inequality too.”