Transport Inequalities. A Survey
2010, v.16, Issue 4, 635-736
This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory.
Keywords: transport inequalities,optimal transport,relative entropy,Fisher information,concentration of measure,deviation inequalities,logarithmic Sobolev inequalities,inf-convolution inequalities,large deviations