Multivariate CLT perhaps? The precondition seems like it might be a bit less common than the regular central limit theorem, but still plausible, if you assume x and y are correlated by being affected by a third factor, z, which controls the terms that sum together to make x and y.
Once you have a multivariate normal distribution, you’re good, since they always have (hyper-)elliptical envelopes.
Multivariate CLT perhaps? The precondition seems like it might be a bit less common than the regular central limit theorem, but still plausible, if you assume x and y are correlated by being affected by a third factor, z, which controls the terms that sum together to make x and y.
Once you have a multivariate normal distribution, you’re good, since they always have (hyper-)elliptical envelopes.