I am looking for applications of the notion of [Gromov-Hausdorff convergence][1] to prove theorems that a priori have nothing to do with it. Examples that I am aware of (thanks to wikipedia and google):

* [Gromov's theorem][2] 

* The [wikipedia][3] page links to a [paper][4] that uses GH convergence to prove a stability result in cosmology.

What are more examples? Ideally they would be along the lines of Gromov's theorem, or proofs of geometric facts, but I'm interested to hear about anything.

As a subquestion, are there interesting applications of [Gromov's compactness theorem][5] to prove results about manifolds with bounded Ricci which have nothing to do with GH convergence? 

 [1]: https://en.wikipedia.org/wiki/Gromov%E2%80%93Hausdorff_convergence
 [2]: https://en.wikipedia.org/wiki/Gromov's_theorem_on_groups_of_polynomial_growth
 [3]: https://en.wikipedia.org/wiki/Gromov%E2%80%93Hausdorff_convergence
 [4]: https://doi.org/10.1007/s00039-004-0477-4
 [5]: https://en.wikipedia.org/wiki/Gromov's_compactness_theorem_(geometry)