Localisation and delocalisation in the parabolic Anderson model
Nadia Sidorova (University College London)
Abstract: 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.
mathematical physicsprobability
Audience: researchers in the topic
Probability and the City Seminar
Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.
Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .
Organizers: | Ivan Z Corwin*, Eyal Lubetzky* |
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