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Oct 24, 2017 at 13:48 vote accept Igor Rivin
Oct 24, 2017 at 13:46 vote accept Igor Rivin
Oct 24, 2017 at 13:47
Oct 24, 2017 at 9:38 answer added Brendan McKay timeline score: 2
Oct 23, 2017 at 23:53 answer added Henry timeline score: 3
Oct 23, 2017 at 1:59 history edited Igor Rivin CC BY-SA 3.0
added experimental wisdom.
Oct 22, 2017 at 21:21 comment added Igor Rivin @JamesMartin Yes, the body asked for the distribution, the title for the expectation, I was spreading confusion :)
Oct 22, 2017 at 20:25 comment added James Martin Ah, I see. At the time I made my comment, the title of the question was "The expected number of chord intersections". So it's somewhat natural that both usul and I thought that you wanted the expected number :)
Oct 22, 2017 at 18:33 history edited Igor Rivin CC BY-SA 3.0
clarified the statement
Oct 22, 2017 at 18:32 comment added Igor Rivin @JamesMartin usul gives the expectation, I ask for the distribution...
Oct 22, 2017 at 18:20 comment added James Martin @IgorRivin Then you should make that clear in the question! There are lots of ways to choose "random chords". In particular, the model referred to in the post you quoted has chords produced by two uniform points in the disc, rather than two uniform points on the perimeter. (Possibly it was edited since you wrote your question?) In any case, for two uniform points on the circle, usul has a nice simple answer below.
Oct 22, 2017 at 15:57 answer added usul timeline score: 4
Oct 22, 2017 at 15:52 comment added Igor Rivin @GerhardPaseman The chords come from $2n$ uniform points on the circle, so the lengths are what they are...
Oct 22, 2017 at 15:33 comment added Gerhard Paseman It really depends on how chord lengths are distributed. For any collection of n chords (with no length appearing more than twice, and none a diameter), you can get from 0 to n choose 2 intersections by rotating chords individually. However, if they are all small , 0 is more likely, and if they are all near the length of a diameter, n choose 2 is more likely. Gerhard "You Might Use Circular Reasoning" Paseman, 2017.10.22.
Oct 22, 2017 at 15:22 history asked Igor Rivin CC BY-SA 3.0