On the Regularity of the Conditional Distribution of the Sample Mean

#### V. Chulaevsky

2015, v.21, Issue 3, 415-431

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 \cite{C10} in the context of the eigenvalue concentration analysis for multi-particle
random operators, is satisfied for a class of probability distributions
with sufficiently smooth probability density.
It generalizes a well-known property of Gaussian IID samples.

Keywords: sample mean, conditional distribution, regularity