This chapter gives some techniques for proving superconcentration and chaos in discrete problems that fall outside the Gaussian setting. The method is based mainly on the so-called “independent flips” semigroup and associated hypercontractive inequalities, such as the Bonami-Beckner inequality, and the equivalence of superconcentration and chaos in the discrete setting.
KeywordsMarkov Process Random Vector Dirichlet Form Equilibrium Measure Uniform Measure
- Chatterjee, S.: Disorder chaos and multiple valleys in spin glasses. Preprint (2009). Available at http://arxiv.org/abs/0907.3381