I am confused by this line from a paper:
"Let $F_1(x)$ be the cumulative distribution of the magnitude of an $n$−dimensional standard Gaussian random variable and $F_2(x)$ be the cumulative distribution of the magnitude of a random point in a Euclidean unit ball of radius $r$"
Can someone explain to me what $F_1(x)$ and $F_2(x)$ is? Thanks a lot!
The paper is here: http://www.mit.edu/~har/Dikin.pdf (page 9)
I would also really really appreciate it if someone has the time to explain to me how to sample from this Dikin ellipsoid. I think I've fully understood the definitions, but the part about the pseudo-inverse and vector scaling seems confusing.
Edit: I know how to sample points from the $n$-dimensional Gaussian and the $n$-dimensional Euclidean ball. But it seems to me that $F_1$ and $F_2$ are invertible functions?