An Information-Geometric Program for AM-GM Stability: Log-Sobolev Bounds and Variance Control
Year: 2025
Type: article
Abstract: This work proposes and develops an information-geometric program to establish a quantitative stability bound for the Arithmetic Mean– Geometric Mean (AM-GM) inequality De Ceuster [2025b]. We combine tools from information geometry, optimal transport, and functional inequalities (specifically the Log-Sobolev inequality, LSI). The core philosophy is to translate additive dispersion (variance σ2) into multiplicative deviation (log(A/G)) via probabilistic metrics. We formulate a sufficient-condition theorem: if an empirical distribution satisfies an LSI, an explicit exponential bound for the AM/GM ratio follows.
Author: de ceuster, peter
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7090851208
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