Small ball probabilities, maximum density and rearrangements

2015/03/31 by Tomas Juškevičius, T. Juškevičius, J. D. Lee +2 · 1 citation
Chemistry · Mathematics · #60E05 #60F10 #60G50 #FOS: Mathematics #History and advancements in chemistry #Probability (math.PR) #math.PR #msc:60E05 #msc:60F10 #msc:60G50

paper · pdf · doi:10.48550/arxiv.1503.09190

4 pages; typos corrected

openalex publication_date 2015/03/31 · arxiv created 2015/04/01 · arxiv updated 2015/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the probability that a sum of independent random variables in ℝ^d with bounded densities lies in a ball is maximized by taking uniform distributions on balls. This in turn generalizes a result by Rogozin on the maximum density of such sums on the line.

Cited by

• Rogozin's convolution inequality for locally compact groups

Related

• Small ball probability, Inverse theorems, and applications
• A Short Note on the Average Maximal Number of Balls in a Bin
• Optimal densities of packings consisting of highly unequal objects
• The limit distribution of the maximum probability nearest neighbor ball
• Expected number of uniformly distributed balls in a most loaded bin using placement with simple linear functions