Noise Stability of Functions with Low Influences: Invariance and Optimality II - The Non Reversible Case

By Elchanan Mossel. 2007

307 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c358e32f58a89a89d10ab461ca6274707baa7676

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Citations in the corpus

Introduction to Property Testing (2017, background): “This tester has played a pivotal role in the PCP constructions of [37] as well as in numerous subsequent PCP constructions including those in [170, 171, 249, 95, 186, 187, 211].”
Robust dimension free isoperimetry in Gaussian space (2012, methodology): “(Both of the statements above follow from the arguments of [24].”
Asymptotic independence of multiple Wiener-It\^o integrals and the resulting limit laws (2011, methodology): “16 of [6], the convergence holds in all L( ).”
The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics into 1 (Extended Abstract) (2005, methodology): “A recent improvement of this theorem due to Mossel et al. [ 27 ] improves both of our lower bounds to (log log n)1/4−δ.”
Inapproximability of NP-complete Problems, Discrete Fourier Analysis, and Geometry (2011, methodology): “This follows either from the Majority Is Stablest Theorem [38] that we will describe in the next section or essentially from the Bourgain’s Theorem stated below.”
Decidability of Non-interactive Simulation of Joint Distributions (2016, methodology): “1 is a result about correlation bounds for low influence functions (which are generalizations of the ‘Majority is Stablest’ theorem), which is obtained from the invariance principle [36], [37].”
A generalization of the Lindeberg principle (2005, methodology): “Comparison of f(X1, . . . ,Xn) and f(Y1, . . . , Yn) for polynomial f has been examined by Rotar [16] and Mossel, O’Donnell and Oleszkiewicz [13], and for general smooth f with bounded derivatives by Chatterjee [5].”
Optimal algorithms and inapproximability results for every CSP? (2008, methodology): “In general, the invariance principle requires the ensembles of random variables to be hypercontractive [19, 18].”
Robust Optimality of Gaussian Noise Stability (2012, methodology): “All of these variations, however, are proved in essentially the same way, namely by combining the ideas from [36] with the appropriate Gaussian robustness result.”