Title: Models of Random Knots,
Abstract: 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.