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Localisation and ageing in the parabolic Anderson model

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Periodic and Ergodic Spectral Problems

The parabolic Anderson problem is the Cauchy problem for the heat equation on the d-dimensional integer lattice with random potential. It describes the behaviour of branching random walks in a random environment (represented by the potential) and is being actively studied by mathematical physicists. One of the most important situations is when the potential is time-independent and is 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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