Conformational statistics of randomly-branching double-folded ring polymers

The conformations of topologically constrained double-folded ring polymers can be described as wrappings of randomly branched primitive trees. We extend previous work on the tree statistics under different (solvent) conditions to explore the conformational statistics of double-folded rings in the limit of tight wrapping. In particular, we relate the exponents characterizing the ring statistics to those describing the primitive trees and discuss the distribution functions $p(\vec r | \ell)$ and $p(L | \ell)$ for the spatial distance, $\vec r$, and tree contour distance, $L$, between monomers as a function of their ring contour distance, $\ell$.