Hypocoercive concentration bounds for Stratonovich functionals

Determine whether the concentration bounds for Stratonovich-type functionals can be extended to hypocoercive dynamics that do not satisfy a Poincaré inequality but converge exponentially fast to the stationary state in L²(μ).

Background

The established results assume a Poincaré inequality, whereas hypocoercive systems may exhibit exponential convergence in L²(μ) without satisfying that inequality. The paper notes that Bernstein-type concentration inequalities are known for density-type observables in this setting through a modified inner product, but leaves open whether an analogous extension is possible for Stratonovich-type observables.

References

Moreover, it will be interesting to investigate whether our concentration bounds on Stratonovich-type functionals can be extended to the hypocoervice setting (i.e., dynamics that do not satisfy a Poincaré inequality but converge exponentially fast to the stationary state in L²(μ)), where recently Bernstein-type concentration inequalities have been proven for density-type observables using a modified inner product .

— Concentration of additive functionals of Stratonovich-type  (2609.01581 - Bebon et al., 1 Sep 2026) in Section 'Open questions'