Log-Convexity of Fisher Information Along Heat Flow

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

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probability-statisticsMay 18, 2026Significance 15/100Registry: unreviewed

Log-Convexity of Fisher Information Along Heat Flow

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

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

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