Dependence of v-function estimates and fluctuations on slow/fast boundary dynamics

Determine how the correlation (v-function) estimates and the resulting non-equilibrium fluctuation limit for the stirring process with births and deaths depend on the relative strength of the boundary birth–death dynamics when the boundary dynamics are slowed down or accelerated with respect to the stirring (e.g., rates scaled by N^θ). Analyze the fluctuation behavior across these regimes and identify the explicit dependence on the boundary strength parameter.

Background

Previous hydrodynamic results for related models consider slow boundary dynamics with rates scaled as Nθ. The present work treats fluctuations under a specific, critical scaling where estimates are available, but does not analyze how these estimates (and the limiting field) change with different boundary strengths.

Understanding the explicit dependence on the boundary dynamics parameter would clarify fluctuation regimes and potentially require new bounds for v-functions adapted to slow/fast boundary interactions.

References

We conclude by collecting a few interesting problems, closely related to the ones investigated in this article, that remain open for further study. A second direction is to analyze our results in the case the system is put in contact with slow/fast boundary dynamics and to explore what is the dependence on the strength of the dynamics in the $v$-functions estimates.

— Non-equilibrium fluctuations for the stirring process with births and deaths  (2512.12902 - Birmpa et al., 15 Dec 2025) in Introduction, Future problems