Noise stability of functions with low influences: invariance and optimality

ANNALS OF MATHEMATICS, no. 1 (2010): 295-341

Cited by: 314|Views88
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Abstract

In this paper we study functions with low influences on product probability spaces. These are functions f : Omega(1) x ... Omega(n) -> R that have E[Var(Omega i) [f]] small compared to Var[f] for each i. The analysis of boolean functions f : {-1, 1}(n) -> {-1, 1} with low influences has become a central problem in discrete Fourier analysi...More

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