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.
|Title of host publication||Geometric Aspects of Functional Analysis|
|Subtitle of host publication||Israel Seminar 2006-2010|
|Number of pages||18|
|State||Published - 2012|
|Name||Lecture Notes in Mathematics|