A simple reduction from a biased measure on the discrete cube to the uniform measure
نویسنده
چکیده
We show that certain statements related to the Fourier-Walsh expansion of functions with respect to a biased measure on the discrete cube can be deduced from the respective results for the uniform measure by a simple reduction. In particular, we present simple generalizations to the biased measure μp of the Bonami-Beckner hypercontractive inequality, and of Talagrand’s lower bound on the size of the boundary of subsets of the discrete cube. Our generalizations are tight up to constant factors.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 33 شماره
صفحات -
تاریخ انتشار 2012