Sumners, D. W.; Whittington, S. G. Knots in self-avoiding walks. (English) Zbl 0659.57003 J. Phys. A 21, No. 7, 1689-1694 (1988). 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. Cited in 3 ReviewsCited in 51 Documents 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 Keywords:existence of knots in random self-avoiding walks on a lattice; Kesten’s pattern theorem; three-dimensional simple cubic lattice PDFBibTeX XMLCite \textit{D. W. Sumners} and \textit{S. G. Whittington}, J. Phys. A, Math. Gen. 21, No. 7, 1689--1694 (1988; Zbl 0659.57003) Full Text: DOI