Titlebook: Superconcentration and Related Topics; Sourav Chatterjee Book 2014 Springer International Publishing Switzerland 2014 60E15, 60K35, 60G15,

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Further Applications of Hypercontractivity,This chapter gives a number of further applications of hypercontractivity to prove superconcentration, including an application to the largest eigenvalue in the Gaussian Unitary Ensemble of random matrices.

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The Interpolation Method for Proving Chaos,This chapter introduces the “interpolation method” for proving chaos. This method was used by the author to prove chaos in the Sherrington-Kirkpatrick model a few years ago. The proof is reproduced here.

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Variance Lower Bounds,This chapter gives some tools for proving lower bounds on the variance of Gaussian functionals. The methods are applied to understand chaotic behavior in the Edwards-Anderson model of lattice spin glasses.

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Introduction,s. The examples are drawn from first-passage percolation, random polymers and the Sherrington-Kirkpatrick model of spin glasses. The concept of asymptotic essential uniqueness, introduced by David Aldous, is briefly discussed.

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https://doi.org/10.1007/978-3-319-03886-560E15, 60K35, 60G15, 82B44, 60G60, 60G70; Gaussian field; chaos; concentration of measure; disordered sy

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