Talagrand’s Method for Proving Superconcentration
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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