We survey several Talagrand type inequalities and their application to influences with the tool of hypercontractivity for both discrete and continuous, and product and non-product models. The approach covers similarly by a simple interpolation the framework of geometric influences recently developed by N. Keller, E. Mossel and A. Sen. Geometric Brascamp-Lieb decompositions are also considered in this context. © 2012 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Cordero-Erausquin, D., & Klartag, B. (2012). Interpolations, convexity and geometric inequalities. Lecture Notes in Mathematics. Springer Verlag. https://doi.org/10.1007/978-3-642-29849-3_9
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