Determine annealed survival asymptotics in dimensions three and higher

Determine the correct large-time asymptotics of the annealed survival probability for a random walk among an inhomogeneous Poisson system of mobile traps in dimensions \(d\geq 3\), including the decay rate and leading asymptotic behavior.

Background

The main annealed-survival theorem establishes precise asymptotics only in dimensions one and two, under bounded initial trap intensities and the condition that the mean trap intensity is minimized at the origin. The paper does not obtain corresponding asymptotics in dimensions $d\geq3$. In these dimensions the random walk is transient, so the confinement strategy used to match lower and upper bounds in low dimensions no longer gives sharp estimates.

The lack of time reversibility in the inhomogeneous trap field also prevents a direct application of the parabolic Anderson model and subadditivity methods used in homogeneous environments. The authors mention level-three large deviations together with Varadhan's lemma as one possible route, but no such argument is completed.