In the context of the error vector $$\epsilon: \Omega \to \mathbb R^n$$ of a multivariable regression, I have heard roughly the following:
The distribution of $\epsilon$ is uniform over the angle, so the random vector is equally likely to point in any direction. Distributions other than the Gaussian one don't give a spherically symmetrical distribution.
As far as I can tell, it says that the multivariable normal distribution can be characterized in this way. It made me very curios. I was looking for a proof and saw this:
Among spherically symmetric distributions are not only multivariate normal distributions with covariance matrices of form $σ^2I$ but also, for example, certain cases of standard multivariate t and logistic distributions.
So the first quote is wrong and there is nothing special about normal distribution in this regard?