For divergent sequences of Schottky groups of the N-dimensional hyperbolic space HN, the Hausdorff dimension of the limit sets typically goes to zero. By considering actions of these groups on the infinite-dimensional hyperbolic space, we give an asymptotic for this convergence.
This is joint work with Gilles Courtois. It is partly inspired by recent work of Dang-Mehmeti. If time permits, I will compare the two approaches.
Fanny Kassel