Abstract
This chapter introduces a new method for proving superconcentration, based on an improved Poincaré inequality. The author calls this the “spectral method”. The spectral method is used to give a short proof of superconcentration in the Sherrington-Kirkpatrick model, substantially simplifying the original proof given by the author some years ago.
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Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58, 13–30 (1963)
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Chatterjee, S. (2014). The Spectral Method for Proving Superconcentration. In: Superconcentration and Related Topics. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-03886-5_6
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DOI: https://doi.org/10.1007/978-3-319-03886-5_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03885-8
Online ISBN: 978-3-319-03886-5
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