Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential
Ryoki Fukushima, Naomasa Ueki
TL;DR
This paper investigates the long-term behavior of solutions to the parabolic Anderson problem with a perturbed lattice potential, deriving moment asymptotics and showing concentration phenomena in the solution's total mass.
Contribution
It provides new asymptotic formulas for moments of the solution's total mass in a perturbed lattice potential setting.
Findings
Total mass asymptotics are derived for the solution.
The solution's total mass concentrates on a small set in configuration space.
The results reveal the influence of long-tailed potentials on solution behavior.
Abstract
The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied. The moment asymptotics of the total mass of the solution is derived.The results show that the total mass of the solution concentrates on a small set in the space of configuration.
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