Gotcha. The non-linearity part “breaking” things makes sense. The main uncertainty in my head right now is whether repeatedly convolving in 2d would require more convolutions to get near gaussian than are required in 1d—like, in dimension m, do you need m times as many distributions; more than m times as many,;or can you use the same amount of convolutions as you would have in 1d? Does convergence get a lot harder as dimension increases, or does nothing special happen?
Gotcha. The non-linearity part “breaking” things makes sense. The main uncertainty in my head right now is whether repeatedly convolving in 2d would require more convolutions to get near gaussian than are required in 1d—like, in dimension m, do you need m times as many distributions; more than m times as many,;or can you use the same amount of convolutions as you would have in 1d? Does convergence get a lot harder as dimension increases, or does nothing special happen?