In this talk we will give an introduction to Assouad dimension and consider several models of random fractals. We will show that, in general, the Assouad dimension is almost surely as high as possible. This is contrary to other notions of dimension, like Hausdorff, box and packing dimension, which are usually given by some form of 'weighted average'. Random sets covered will include self-similar, Bedford-McMullen (self-affine) random constructions and Mandelbrot percolations.
(Joint work with Jonathan Fraser and Jun Jie Miao.)