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Talagrand’s Method for Proving Superconcentration

  • Sourav Chatterjee
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter is devoted to the theory and applications of Talagrand’s method for proving superconcentration using hypercontractivity, a method that builds on a key insight of Kahn, Kalai and Linial. One of the new results proved here says that Talagrand’s method is “necessary and sufficient” for proving superconcentration of monotone functions. The application of Talagrand’s method to first-passage percolation, involving an original idea of Benjamini, Kalai and Schramm, is worked out. A second application to directed polymers is also worked out.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sourav Chatterjee
    • 1
  1. 1.Department of StatisticsStanford UniversityStanfordUSA

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