A simple reduction from a biased measure on the discrete. cube to the uniform measure

作者：Keller Nathan^*

来源：European Journal of Combinatorics, 2012, 33(8): 1943-1957.

DOI：10.1016/j.ejc.2012.06.003

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 pp of the Bonami-Beckner hypercontractive inequality, and of Talagrand%26apos;s lower bound on the size of the boundary of subsets of the discrete cube. Our generalizations are tight up to constant factors.

• 出版日期2012-11