This is a follow-up to [this question:](https://mathoverflow.net/questions/283987/the-largest-piece-of-circumference/283999#283999) Given $n$ random chords of a circle, what is the distribution of the number of intersections? Random is defined by "endpoints uniform on the circle".


**Update** Numerical experiments indicate that the distribution converges to a gaussian.



The distribution of the number of chord intersections
The number of crossings in a chord diagram depends only on the order that the ends of the chords appear on the circle. Also, for any chord diagram every pairing of the $2n$ endpoints is equally likely. Therefore, it suffices to take any $2n$ distinct points on the circle and pair them at random.


This is a widely studied problem. A survey and the asymptotic distribution of the number of crossings appears [in this paper](https://link.springer.com/chapter/10.1007/978-3-662-04166-6_17) (note the ridiculous price Springer wants for this conference proceedings), and can be read for free [here](http://algo.inria.fr/flajolet/Publications/FlNo00.pdf). 


