Self-affine carpets on the square lattice (with Y. Peres). Combinatorics, Probability and Computing, 6, 197-204 (1997)

We explore the `Hausdorff dimension at infinity' for self-affine carpets defined on the square lattice. This notion of dimension (due to Barlow and Taylor), which is the correct notion from a probabilistic perspective, differs for these sets from more `naive' indices of fractal dimension.