Localisation and ageing in the parabolic Anderson model with Weibull potential (Q400578)

The parabolic Anderson model has been proposed by \textit{P. W. Anderson} [``Absence of diffusion in certain random lattices'', Phys. Rev. 109, 1492--1505 (1958; \url{doi:10.1103/PhysRev.109.1492})] to describe electron localization inside a semiconductor. Mathematically, it is a Cauchy problem for a parabolic partial differential equation which involves a random potential which is a collection of independent identically distributed random variables.NEWLINENEWLINEThe authors study the asymptotic behavior of the solution and a complete localization result is stated as time increases to infinity. They use a point process approach and give some results on the negligible paths of the random walk.