Quantify the effects of free-path correlations on temporal variance and reverberation decay

Quantify the contribution of correlations between successive wall-to-wall free paths to the growth of the temporal variance of cumulative propagation times and to reverberation decay in diffuse sound fields.

Background

The paper’s independent-renewal approximation neglects correlations between successive wall-to-wall free paths, although ray-tracing simulations show positive correlations even after the reflection-order-dependent mean free path has approached its stationary value. The simulations also find that the temporal variance of wall-collision times grows more rapidly than predicted by an independent sequence having the same marginal free-path variance.

The unresolved issue is to determine quantitatively how these correlations alter cumulative propagation-time variance and, in turn, the predicted reverberation decay. Resolving this issue would clarify the limitations of the independent-renewal approximation and establish when marginal free-path statistics are sufficient for reverberation prediction.

References

Quantifying the contribution of correlations to this variance growth and to reverberation decay remains a subject for future work.

— Statistical foundations of revised reverberation theory for a diffuse sound field in a room  (2610.21826 - Hanyu, 15 Oct 2026) in Section VII.B, “Free-path statistics and assessment of the renewal approximation”

The extent to which correlation effects and distributional approximations contribute to the remaining prediction errors is not resolved by the present comparisons.

— Statistical foundations of revised reverberation theory for a diffuse sound field in a room  (2610.21826 - Hanyu, 15 Oct 2026) in Section VII.D, “Reverberation-time prediction accuracy in the practical absorption range”