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Localisation and delocalisation in the parabolic Anderson model

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  • UserNadia Sidorova (University College London)
  • ClockMonday 13 May 2019, 15:00-16:00
  • HouseCMS, MR13.

If you have a question about this talk, please contact Ivan Moyano .

The parabolic Anderson problem is the Cauchy problem for the heat equation on the integer lattice with random potential. It describes the mean-field behaviour of a continuous-time branching random walk. It is well-known that, unlike the standard heat equation, the solution of the parabolic Anderson model exhibits strong localisation. In particular, for a wide class of iid potentials it is localised at just one point. However, in a partially symmetric parabolic Anderson model, the one-point localisation breaks down for heavy-tailed potentials and remains unchanged for light-tailed potentials, exhibiting a range of phase transitions.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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