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The classical hypercontractive inequality for the noise operator on the discrete cube plays a crucial role in many of the fundamental results in the Analysis of Boolean functions, such as the KKL (Kahn-Kalai-Linial) theorem, Friedgut's junta theorem and the invariance principle of Mossel, O'Donnell and Oleszkiewicz.
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Aline Bonami · 1970
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William Beckner · 1975
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L. Gross · 1975
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G. Margulis · 1977
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Bradley Efron and Charles Stein · 1981
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Every monotone graph property has a sharp threshold
Ehud Friedgut and Gil Kalai · 1996
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Jean Bourgain and Gil Kalai · 1997
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Ehud Friedgut · 1998
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Dimitris Achlioptas and Ehud Friedgut · 1999
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Itai Benjamini, Gil Kalai, and Oded Schramm · 1999
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Ehud Friedgut · 1999
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Irit Dinur, Ehud Friedgut, and Oded Regev · 2008
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N. Fusco, F. Maggi, and A. Pratelli · 2008
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Anders Johansson, Jeff Kahn, and Van Vu · 2008
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Intersecting families are essentially contained in juntas
Irit Dinur and Ehud Friedgut · 2009
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Gaussian bounds for noise correlation of functions
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Ehud Friedgut, Hiêp Hàn, Yury Person, and Mathias Schacht · 2016
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Nathan Keller and Noam Lifshitz · 2017
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Peter Keevash and Eoin Long · 2018
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Elchanan Mossel · 2010
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Noise stability of functions with low influences: Invariance and optimality
Elchanan Mossel, Ryan O’Donnell, and Krzysztof Oleszkiewicz · 2010
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Quantitative noise sensitivity and exceptional times for percolation
Oded Schramm and Jeffrey E Steif · 2010
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Sharp threshold for percolation on expanders
Itai Benjamini, Stéphane Boucheron, Gábor Lugosi, and Raphaël Rossignol · 2012
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A structure theorem for Boolean functions with small total influences
Hamed Hatami · 2012
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The size of a hypergraph and its matching number
Hao Huang, Po-Shen Loh, and Benny Sudakov · 2012
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Approximation of biased Boolean functions of small total influence by DNF’s
Nathan Keller and Noam Lifshitz · 2018
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Small set expansion in the Johnson graph
Subhash Khot, Dor Minzer, Dana Moshkovitz, and Muli Safra · 2018
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Pseudorandom sets in grassmann graph have near-perfect expansion
Subhash Khot, Dor Minzer, and Muli Safra · 2018
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Hypergraph removal lemmas via robust sharp threshold theorems
Noam Lifshitz · 2018
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Spanning trees in random graphs
Richard Montgomery · 2018
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Vertex-isoperimetric stability in the hypercube
Michał Przykucki and Alexander Roberts · 2018
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Noise sensitivity of random walks on groups
Itai Benjamini and Jérémie Brieussel · 2019
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Hypercontractivity for global functions on the bilinear scheme and forbidden intersections
David Ellis, Guy Kindler, and Noam Lifshitz · 2019
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Hypercontractivity for global functions on the slice
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