Concentration of Exponential Tilts Implies Curvature

Aziz Ben Nejma

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arXiv · 2610.34570

Concentration of Exponential Tilts Implies Curvature

Aziz Ben Nejma

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Abstract

We show, under a smoothness assumption, that probability measures whose exponential tilts have a uniformly bounded variance are given by a strongly convex potential, up to a bounded perturbation, yielding a partial converse to the Bakry-Émery theorem combined with Holley-Stroock's perturbation principle. A stronger version enforcing uniform convexity of the potential is obtained by considering the low-temperature regime.

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Aziz Ben Nejma. 2026-10-25. Concentration of Exponential Tilts Implies Curvature. https://arxiv.org/abs/2610.34570

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