Convergence of quenched Lyapunov exponents to the annealed exponent at high mobility

Let $\lambda_p^{u_0}(\kappa)$ denote the quenched Lyapunov exponent of order $p\in\mathbb{N}$ for mobility parameter $\kappa$, and let $\lambda_0^{u_0}(\kappa)$ be the corresponding exponent of order zero. In the population-dynamics interpretation, $\lambda_0^{u_0}(\kappa)$ describes the asymptotic fraction of time that the fastest-growing $B$-particle lineages spend on $A$-particles. High-mobility convergence conjecture. As the mobility parameter tends to infinity, the quenched Lyapunov exponents should merge with the corresponding annealed Lyapunov exponents, in the sense that

$$\lim_{\kappa\to\infty} [\lambda_p^{u_0}(\kappa)-\lambda_0^{u_0}(\kappa)]=0$$

for all $p\in\mathbb{N}$. This predicts that sufficiently rapid motion suppresses the distinction between the quenched exponents of positive order and the order-zero exponent; the source presents it as an expectation, and no resolution is supplied here.