Details

Autor(en) / Beteiligte

• Aizenman, Michael
• Germinet, François
• Klein, Abel
• Warzel, Simone

Titel

On Bernoulli decompositions for random variables, concentration bounds, and spectral localization

Ist Teil von

• Probability theory and related fields, 2009-01, Vol.143 (1-2), p.219-238

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2009

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli component. This observation provides a tool for the extension of results which are known for Bernoulli random variables to arbitrary distributions. Two applications are provided here: (i) an anti-concentration bound for a class of functions of independent random variables, where probabilistic bounds are extracted from combinatorial results, and (ii) a proof, based on the Bernoulli case, of spectral localization for random Schrödinger operators with arbitrary probability distributions for the single site coupling constants. For a general random variable, the Bernoulli component may be defined so that its conditional variance is uniformly positive. The natural maximization problem is an optimal transport question which is also addressed here.