Optimized estimates of the regularity of the conditional distribution of the sample mean

Abstract

We give an improved 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", extending the well-known property of Gaussian IID samples. Specifically, we replace the bounds in probability, established in our earlier works, by those in distribution, and this results in the optimal regularity exponent in the final estimate.

arXiv admin note: substantial text overlap with arXiv:1304.6913

References in corpus (1)

• A remark on charge transfer processes in multi-particle systems

Cited by in corpus (2)

• Characterization of the metal-insulator transport transition for the two-particle Anderson model
• Exponential decay of eigenfunctions in a continuous multi-particle Anderson model with sub-exponentially decaying interaction