### Branching random walks in random environment

Probability Seminar

12th October 2018, 3:30 pm – 4:30 pm

Main Maths Building, SM4

We will consider a branching random walk on a lattice, where the branching rates are locally given by a random potential. Since there are various sources of randomness, the central question is how the system compares to the corresponding averaged versions. When averaging only over branching and migration, the expected number of particles solves a heat equation with a random potential known as the parabolic Anderson model. Over the last decade there has been considerable progress in understanding the latter, driven by the observation that the system exhibits intermittency. In our work we concentrate on the effect of averaging over branching/migration and try to understand

if the particle system is close to the solution of the heat equation. It turns out that the answer will depend essentially on the extreme value behaviour of the underlying potential.

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