Central limit theorems for non-central sections of log-concave product measures and star shaped functions

Details Central limit theorems for non-central sections of log-concave product measures and star shaped functions Central limit theorems for non-central sections of log-concave product measures and star shaped functions

2011-08-25

arxiv.org/abs/1108.5011v2

Mathematics

Probability

9 pages

Scientific paper

A section of a function f defined on Euclidean space is the restriction of f to an affine subspace. We study functions with various regularity properties including independence, convexity and smoothness, and show that sections of these functions far from the origin approximate the normal density function. As a consequence, if X and Y are i.i.d. random variables with mild assumptions on their distribution, then the distribution of X+2Y conditional on the event that X+Y is large, is approximately normal.

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