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Log-Convexity of Fisher Information Along Heat Flow

Probability & statistics · posed by 2015 · disproved

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Statement

For every smooth positive density ff on Rd\mathbb{R}^d, must the Fisher information t↦I(f∗γt)t \mapsto I(f * \gamma_t) be log-convex along the heat flow?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    GPT-5.5 Pro

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    The hexagonal counterexample - a smooth positive Gaussian-decaying density on the plane - was found with GPT-5.5 Pro; tensorization extends the disproof to every dimension at least two.

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