1 research outputs found
Localisation and ageing in the parabolic Anderson model with Weibull potential
The parabolic Anderson model is the Cauchy problem for the heat equation on
the integer lattice with a random potential . We consider the case when
is a collection of independent identically
distributed random variables with Weibull distribution with parameter
, and we assume that the solution is initially localised in the
origin. We prove that, as time goes to infinity, the solution completely
localises at just one point with high probability, and we identify the
asymptotic behaviour of the localisation site. We also show that the intervals
between the times when the solution relocalises from one site to another
increase linearly over time, a phenomenon known as ageing.Comment: Published in at http://dx.doi.org/10.1214/13-AOP882 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org