On the regularity of the conditional distribution of the sample mean

Abstract

We show that the hypothesis of regularity of the conditional distribution of the empiric average of a finite sample of IID random variables, given all the sample "fluctuations", which appeared in our earlier manuscript |1] in the context of the eigenvalue concentration analysis for multi-particle random operators, is satisfied for a class of probability distributions with piecewise-constant or sufficiently smooth probability density. It extends the well-known property of Gausssian IID samples.

References in corpus (1)

• A comprehensive proof of localization for continuous Anderson models with singular random potentials

Cited by in corpus (5)

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• Uniform N-particle Anderson localization and unimodal eigenstates in deterministic disordered media without induction on the number of particles