Random meander model for links (Q6642293)

A random link model is introduced that generalizes meander knots, and combinatorial methods are used to study its properties. The meander diagrams are randomly generated through matching pairs of parentheses, and the random links and their complements in \(S^3\) are analyzed. It is shown that trivial links appear with vanishing probability, no link occurs with probability 1, and there is a lower bound on the number of non-isotopic knots for a given number of crossings. The expected twist number is estimated and used to provide a bound of the expected hyperbolic and simplicial volumes. The combinatorial techniques used include Catalan and Narayana numbers and Zeilberger's algorithm.