Unsplittability of Random Links

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Random linking problems arise in physical situations when there is more than one circular molecule present in a fixed volume, and linking of these molecules becomes possible. Mathematically, this is the linking problem for two or more randomly generated polygons. In this paper, we study the asymptotic case when the number of random polygons of fixed length in a fixed volume tends to infinity, and prove that under certain conditions that the probability that these random polygons form an unsplittable link tends to one.