Conjecture on the asymptotic mean absolute self-linking number of confined random walks and polygons

Let SLSL denote the self-linking number of an oriented uniform random walk or polygon in confined space, and let EE denote expectation. Mean absolute self-linking conjecture. As the number nn of edges increases, one has

E[SL2]E[SL2]=E[SL].\sqrt{E[SL^2]}\sim E[\sqrt{SL^2}]=E[\left|SL\right|].

The observed mean absolute self-linking number grows at rate O(n)O(n), with a fitted coefficient close to the square root of the coefficient governing the mean squared self-linking number. The statement is supported only by the numerical study in the source.

Sources & referencesView supporting material

Primary source

E. Panagiotou, K. C. Millett and S. Lambropoulou, “The linking number and the writhe of uniform random walks and polygons in confined spaces”, arXiv:0907.3805 (2009).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.