Concentration of the ratio between the geometric and arithmetic means
J. M. Aldaz
TL;DR
This paper investigates how the ratio of geometric to arithmetic means concentrates around specific values for certain weighted sequences, revealing underlying probabilistic behaviors.
Contribution
It provides new insights into the concentration properties of the geometric-to-arithmetic mean ratio for weighted sequences.
Findings
Identifies conditions for concentration around specific values
Shows dependence on weight sequences
Provides theoretical bounds and probabilistic analysis
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.
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