The Length Scale of $3$-Space Knots, Ephemeral Knots, and Slipknots in Random Walks
نویسندگان
چکیده
منابع مشابه
The length scale of 3-space knots, ephemeral knots, and slipknots in random walks
The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a small knot, an ephemeral knot, or a slipknot goes to one as the length goes to infinity. The probability that a polygon or walk contains a “global” knot also goes to one as the length goes to infinity. What immerges is a highly complex picture of the length scale of knotting in polygons and wa...
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The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a knot goes to one at the length goes to infinity. Here, we prove that this is also true for slipknots consisting of unknotted portions, called the slipknot, that contain a smaller knotted portion, called the ephemeral knot. As is the case with knots, we prove that any topological knot type occu...
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Introduction: A knot is a non-intersecting closed curved in 3-space. The projection of a knot onto the plane yields a knot diagram of the knot. The crossing number of a knot is the minimum number of self-crossings a knot has among all its knot diagrams. We may manipulate a given knot diagram by twisting and moving the curve so that the new diagram obtained after such manipulations is still that...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics Supplement
سال: 2011
ISSN: 0375-9687
DOI: 10.1143/ptps.191.182