This news article describes a recent PNAS paper on this very issue.
Knot formation had been studied a lot by mathematicians, but not much by physicists. Smith was worried that the work wouldn't be taken seriously, but it ended up being published in the prestigious Proceedings of the National Academy of Sciences.
"The way that you get a knot is the string has to bend back on itself, coil back on itself," Smith said. As a string or cord tumbles, the end of it has a 50 percent chance of weaving to the left or the right of the coils, and under or over the coils, sort of like random braiding, Smith said.
The exact citation for this paper (which none of these popular newspapers ever give) is:
Dorian M. Raymer and Douglas E. Smith, PNAS v.104, p.16432 (2007).
Don't get all tied up with it.