30 research outputs found
Classical and quantum behavior of the integrated density of states for a randomly perturbed lattice
The asymptotic behavior of the integrated density of states for a randomly
perturbed lattice at the infimum of the spectrum is investigated. The leading
term is determined when the decay of the single site potential is slow. The
leading term depends only on the classical effect from the scalar potential. To
the contrary, the quantum effect appears when the decay of the single site
potential is fast. The corresponding leading term is estimated and the leading
order is determined. In the multidimensional cases, the leading order varies in
different ways from the known results in the Poisson case. The same problem is
considered for the negative potential. These estimates are applied to
investigate the long time asymptotics of Wiener integrals associated with the
random potentials.Comment: 27 page
Moment asymptotics for the parabolic Anderson problem with a perturbed lattice potential
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