Connect $n$ random points on a sphere in a cycle of
segments between succesive points:

I would like to know the growth rate, with respect to $n$, of the crossing number
(the minimal number of crossings of any diagram of the knot)
$c(n)$ of such a knot.
I only know that $c(n)$ is $O(n^2)$,
because it is known
that the crossing number is upper-bounded by
*the stick number* $s(n)$:
$$\frac{1}{2}(7+\sqrt{ 8 c(K) + 1}) \le s(K)$$
for any knot $K$.
And $s(n) \le n$ is immediate.

I feel certain this has been explored but I am not finding it in the literature. Thanks for pointers!