Concentration of the ratio between the geometric and arithmetic means

Abstract

We explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights one does obtain concentration, around a value that depends on the sequence.

10 pages

Cited by in corpus (4)

• A refinement of the inequality between arithmetic and geometric means
• Sharp bounds for the difference between the arithmetic and geometric means
• A monotonicity property of variances
• The Maclaurin inequality through the probabilistic lens