Wait, wouldn't this result in the opposite of what you want? You want to shift the distribution out, not crowd the center, so you probably want to square your random instead.

Squaring numbers in (0,1) makes them smaller, pulling the random radius closer to center. As an example consider 0.9. Squaring it gets 0.81 vs 0.949 taking the square root.

Because the numbers are less than 1 sqrt pulls them towards 1 (the edge)

assuming random() returns values 0<=r<=1, sqrt will shift the distribution outward