PreprintCC BY-NC-ND 4.0HAL
Concentration of Exponential Tilts Implies Curvature
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.
Related
- Thin-Shell implies small-ball deviation via Gaussian tilts
- Algebraic Localization Implies Exponential Localization in Non-periodic Insulators
- Equivalence on exponential families as Hessian manifolds and classification of exponential families of order 1 with constant Hessian sectional curvature
- Ollivier curvature, isoperimetry, concentration, and log-Sobolev inequality
- Curvature-Dependent Path Concentration in Stochastic Fast-Slow Systems with Noise on the Slow Variable
BibTeX
@misc{nejma2026concentration,
title = {{Concentration of Exponential Tilts Implies Curvature}},
author = {Aziz Ben Nejma},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34570},
eprint = {2610.34570},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05840953v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Concentration of Exponential Tilts Implies Curvature
AU - Aziz Ben Nejma
PY - 2026
DA - 2026/10/25
PB - HAL
DO - 10.48550/arxiv.2610.34570
UR - https://hal.science/hal-05840953v1
AB - 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.
ER -