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Knots in self-avoiding walks. (English) Zbl 0659.57003

In this paper we discuss the existence of knots in random self-avoiding walks on a lattice. using Kesten’s pattern theorem, we show that almost all sufficiently long self-avoiding walks on the three-dimensional simple cubic lattice contain a knot.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
60G50 Sums of independent random variables; random walks
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