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Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces.
Logarithmic sobolev inequalities
L. Gross · 1975
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Every connected regular graph of even degree is a Schreier coset graph
J.L. Gross · 1977
Earlier work this paper cites.
Positivity improving operators and hypercontractivity
C. Borell · 1982
Earlier work this paper cites.
The influence of variables on Boolean functions
J. Kahn, G. Kalai, and N. Linial · 1988
Earlier work this paper cites.
Concentration of measure and isoperimetric inequalities in product spaces
M. Talagrand · 1995
Earlier work this paper cites.
Logarithmic Sobolev inequalities for finite Markov chains
P. Diaconis and L. Saloff-Coste · 1996
Cited alongside, same era.
Boolean functions with low average sensitivity depend on few coordinates
E. Friedgut · 1998
Cited alongside, same era.
The unique games conjecture, integrality gap for cut problems and embeddability of negative type metrics into ℓ 1 \ell_{1}
Subhash Khot and Nisheeth K. Vishnoi · 2005
Cited alongside, same era.
On distance scales, embeddings, and efficient relaxations of the cut cone
James R. Lee · 2005
Cited alongside, same era.
Expander flows, geometric embeddings and graph partitioning
Sanjeev Arora, Satish Rao, and Umesh V. Vazirani · 2009
Later among the works it cites.
3-bit dictator testing: 1 vs. 5/8
Ryan O’Donnell and Yi Wu · 2009
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KKL, Kruskal-Katona, and monotone nets
R. O’Donnell and K. Wimmer · 2009
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Breaking the Multicommodity Flow Barrier for O ( log n ) O(\sqrt{\log n}) -Approximations to Sparsest Cut
J. Sherman · 2009
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