Statistics Seminars: Localisation and ageing in the parabolic Anderson model
15 October 2012 14:00 in CM221
The parabolic Anderson problem is the Cauchy problem for the heat equation on the d-dimensional integer lattice with random potential. It describes mass transport through a random field of sinks and sources and is being actively studied by mathematical physicists. One of the most important situations is when the potential is time-independent and is represented by a collection of independent identically distributed random variables. We discuss the intermittency effect occurring for such potentials and consisting in increasing localisation and randomisation of the solution. We also discuss the ageing behaviour of the model showing that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time.
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