Concentration inequalities and self-averaging

In recent years several concentration inequalities for product measures (and beyond) have been proven under a variety of assumptions. Some of these concentration inequalities are presented in Appendix A.3. An important 

Concentration inequalities require assumptions on tu and in this sense they yield weaker results. However, they give explicit boimds on the probability of deviation from the typical behavior and this is very important both on a conceptual level and for applications. 

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