Passage-time decorrelation conjecture in the chaotic regime

Let $T_0$ and $T_t$ be the passage times at perturbation times $0$ and $t$, and write $\operatorname{Var}(T)$ for the variance of the passage time and $\operatorname{Corr}(T_0,T_t)$ for their correlation. Let $n$ tend to infinity. Passage-time decorrelation conjecture. If

$$t \gg \frac{1}{n}\operatorname{Var}(T),$$

then

$$\operatorname{Corr}(T_0,T_t)=o(1).$$

This predicts decorrelation of passage times in the chaotic regime, at the same scale as the transition from stable to chaotic geodesic behavior. The source notes that related results are not known and motivates the conjecture heuristically through KPZ scaling relations.