Zero-SNR Analyticity of the Scalar MMSE Is Equivalent to Gaussianity

arXiv:2609.15048 · cs.IT, cs.LG, math.IT · Submitted 2026-09-14 · Read on arXiv

cs.IT, cs.LG, math.IT

Submitted: 2026-09-14

Updated: 2026-09-14

Comments: 33 pages, 1 figure

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Non-Gaussianity — 2× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Selection Bias — 1× in this paper · explained in 4 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Measuring Information from Moments
• Introduction to 1-summability and resurgence

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