Abstract

W ( ; ) := inf 2 ( ; ) sZZ 1 2 d(x; y)2 d (x; y); where d(x; y) = kx yk2 and ( ; ) denotes the set of all probability measures on R R with marginals and , i.e., ( R) = and (R ) = . The transportation cost inequality (TCI) obtained by M. Talagrand [15] is W ( ; ) p S( ; ) ; where is the standard Gaussian measure and is any probability measure on R. Recently Talagrand's inequality and its counterpart, the logarithmic Sobolev inequality have received a lot of attention and they have been extended from the Euclidean spaces to Riemannian manifolds. (Contrary to Talagrand's inequality, the logarithmic Sobolev inequality (LSI) gives an upper bound for the

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.