On the Converse of Talagrand's Influence Inequality
نویسندگان
چکیده
In [Tal94], Talagrand showed a generalization of the celebrated KKL theorem. In this work, we prove that the converse of this generalization also holds. Namely, for any sequence of numbers 0 < a1, a2, . . . , an ≤ 1 such that ∑n j=1 aj/(1 − log aj) ≥ C for some constant C > 0, it is possible to find a roughly balanced Boolean function f such that Infj [f ] < aj for every 1 ≤ j ≤ n.
منابع مشابه
Talagrand's Inequality
Notes on Talagrand's inequality. This material is a mixture from Talagrand's two famous papers and Ledoux.
متن کاملA Free Analogue of the Transportation Cost Inequality on the Circle
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 counter...
متن کاملTalagrand's Inequality and Locality in Distributed Computing
We illustrate the use of Talagrand’s inequality and an extension of it to dependent random variables due to Marton for the analysis of distributed randomised algorithms, specifically, for edge colouring graphs.
متن کاملConcentration inequalities using the entropy method
We investigate a new methodology, worked out by Ledoux and Mas-sart, to prove concentration-of-measure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general ready-to-use inequalities. One of these inequalities may be considered as an exponential version of the Efron-Stein inequality. The main purpose of this paper is to p...
متن کاملThe Family Background of Inequality in Educational Opportunities (A case Study of female high school students in Ahar
Inequality of educational opportunities underlies the reproduction of social inequalities and deepens the gap of classes. The origin of the class can be one of the effective factors involved in. The aim of this paper is the study of the impact of family background on inequality of educational opportunities among students. We used the survey method and a questionnaire. We collected needed inform...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1506.06325 شماره
صفحات -
تاریخ انتشار 2015