High-dimensional ellipsolds converge to Gaussian spaces

This talk is based on a joint work with Daisuke Kazukawa (Osaka University).
One of our main theorems states that any sequence of ellipsoids (possibly with unbounded dimension) has a subsequence converging to an (infinite-dimensional) Gaussian space in Gromov's concentration/weak topology. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where ‘irreducible nontrivial’ roughly means to be not constructed from Lévy families nor box convergent sequences.