KNOTS, SLIPKNOTS, AND EPHEMERAL KNOTS IN RANDOM WALKS AND EQUILATERAL POLYGONS

被引：15

作者：

Millett, Kenneth C. ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2010年 / 19卷 / 05期

关键词：

Knots; slipknots; random walks; equilateral polygons; SELF-AVOIDING WALKS; ENTANGLEMENT COMPLEXITY; SCALING BEHAVIOR; TOPOLOGY; PROTEINS; POLYMER; SPACE;

D O I：

10.1142/S0218216510008078

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 occurs as the ephemeral knotted portion of a slipknot.

引用

页码：601 / 615

页数：15

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