### 7 maj 2007, kl 13.15-14.15, Uppsala, Ångström, sal 64119.

### Thomas Jordan (University of Warwick):
The dimension of randomly perturbed self-affine sets

**Abstract.**
The Hausdorff dimension of self-similar sets satisfying the open set
condition is well known. However in the self-affine case the situation, even
with the open set condition, is much more complicated. The Hausdorff
dimension is not necessarily continuous with parameters for the self-affine
set. Over 15 years ago Falconer calculated a formula for the Hausdorff
dimension of self-affine sets which holds generically (I will make it clear
what this means) assuming the norms of the matrices are smaller than 1/2. We
will look at the case of adding random errors to the iterated function
system. In this case for suitably chosen random errors Falconer's formula
holds almost surely with no assumption on the norm.