We review recent theoretical studies on the statistical and dynamical properties of polymers
with nontrivial structures in chemical connectivity and those of polymers with a nontrivial …

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 …

We define the knotting probability of a knot K by the probability for a random polygon or self-
avoiding polygon (SAP) of N segments having the knot type K. We show fundamental and …

We study random knotting by considering knot and link diagrams as decorated,(rooted)
topological maps on spheres and pulling them uniformly from among sets of a given number …

By performing Monte Carlo sampling of N-steps self-avoiding polygons embedded on
different Bravais lattices we explore the robustness of universality in the entropic, metric, and …

Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van
Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-type K lattice …

We use a simple physical map** to adapt the known asymptotic expressions for the
knotting probabilities of self-avoiding polygons to the case of semiflexible rings of beads. We …

We study several related models of self-avoiding polygons in a tubular subgraph of the
simple cubic lattice, with a particular interest in the asymptotics of the knotting statistics …

We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of
impermeable cylindrical segments corresponds to the screening length of double-stranded …

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