Models of random knots
Models of random knots
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DOI：
10.1007/s41468-017-0007-8
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发表时间：
2017-11
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通讯作者：
Chaim Even-Zohar
中科院分区：
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作者：
Chaim Even-Zohar
从概率的角度对结和链接的研究提供了对“典型”结的行为的洞察，并为结和其他具有有趣性质的拓扑对象的新构造开辟了道路。随机曲线的打结也出现在自然科学的应用中，例如在聚合物结构的背景下。我们在这里提出了几个已知的和新的随机化的结和链模型。我们回顾了每个模型中结分布的主要已知结果。我们讨论了这些模型的性质和它们产生的结的性质。我们特别感兴趣的是随机结点的有限型不变量，以及最近研究的Petaluma模型。我们报告了关于这类结不变量渐近分布的严密结果和数值实验。我们的方法提出了各种随机结模型的普遍性和分类问题。
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of “typical” knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of random curves arises also in applications to the natural sciences, such as in the context of the structure of polymers. We present here several known and new randomized models of knots and links. We review the main known results on the knot distribution in each model. We discuss the nature of these models and the properties of the knots they produce. Of particular interest to us are finite type invariants of random knots, and the recently studied Petaluma model. We report on rigorous results and numerical experiments concerning the asymptotic distribution of such knot invariants. Our approach raises questions of universality and classification of the various random knot models.