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Knots in random walks. (English) Zbl 0681.57001

Summary: For even \(n\geq 4\), let \(\pi_ n\) denote the probability that a random self-avoiding polygon of n steps on the three-dimensional cubic lattice is unknotted. We show that \(\pi_ n^{1/n}\to C\) as \(n\to \infty\), for some constant \(C<1\).

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
60G50 Sums of independent random variables; random walks
82D60 Statistical mechanics of polymers
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