Probability and Mathematical Physics Seminar

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In this talk I discuss two “driven diffusive systems”, that is models that combine diffusive effects with a forcing mechanism. The first is a diffusion given by the SDE

dXt = F (Xt)dt + dBt

where F is a random drift field and the second is an SPDE given by

∂tu = ∆u + (w · ∇u2) + ∇ · ξ,

where w is a fixed vector, and ξ is space-time white noise.

The large scale behaviour of these models depends highly on the dimension. In dimension 3 and higher, the diffusive effects prevail, while in dimension 1 the nonlinearity dominates. In the scaling critical dimension 2 the behaviour is more subtle and a logarithmic correction to the diffusivity occurs. 

In the talk I will show how to use Fock space analysis to show this behaviour and give an overview of other results in this area. In particular I will contrast the two different universality classes of these models.