Conjecture on the asymptotic mean absolute self-linking number of confined random walks and polygons
Conjecture on the asymptotic mean absolute self-linking number of confined random walks and polygons
Let denote the self-linking number of an oriented uniform random walk or polygon in confined space, and let denote expectation. Mean absolute self-linking conjecture. As the number of edges increases, one has
The observed mean absolute self-linking number grows at rate , 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).
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