Journals Information
Mathematics and Statistics Vol. 3(2), pp. 46 - 52
DOI: 10.13189/ms.2015.030204
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Optimized Regularity Estimates of Conditional Distribution of the Sample Mean
Victor Chulaevsky *
Department of Mathematics, University of Reims Champagne-Ardenne, B.P. 1039 51687 Reims Cedex 2, France
ABSTRACT
We prove an optimized estimate for the regularity of the conditional distribution of the empiric mean of a finite sample of IID random variables, conditional on the sample "fluctuations". Prior results, based on bounds in probability, provided a Hölder-type regularity of the conditional distribution. We establish a Lipschitz regularity, using bounds in expectation. The new estimate, extending a well-known property of Gaussian IID samples, is a crucial ingredient of the Multi-Scale Analysis of multi-particle Anderson-type random Hamiltonians in a Euclidean space. In particular, the H¨older regularity of the multi-particle eigenvalue distribution, sufficient for the localization analysis of N-particle lattice Hamiltonians, with N ≥ 3, needs to be replaced by Lipschitz regularity for similar Hamiltonians in the Euclidean space.
KEYWORDS
Multi-particle Anderson Localization, Eigenvalue Concentration Estimates
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Victor Chulaevsky , "Optimized Regularity Estimates of Conditional Distribution of the Sample Mean," Mathematics and Statistics, Vol. 3, No. 2, pp. 46 - 52, 2015. DOI: 10.13189/ms.2015.030204.
(b). APA Format:
Victor Chulaevsky (2015). Optimized Regularity Estimates of Conditional Distribution of the Sample Mean. Mathematics and Statistics, 3(2), 46 - 52. DOI: 10.13189/ms.2015.030204.