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On the regularity of the conditional distribution of the sample mean

Mathematical Physics 2013-11-19 v3 math.MP

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.

Keywords

Cite

@article{arxiv.1304.6913,
  title  = {On the regularity of the conditional distribution of the sample mean},
  author = {Victor Chulaevsky},
  journal= {arXiv preprint arXiv:1304.6913},
  year   = {2013}
}