Title: Randomly cross-linked polymer models,
Abstract: Polymer models are used to describe chromatin, which can be folded at
different spatial scales by binding molecules. By folding, chromatin generates
loops of various sizes. We present here a randomly cross-linked (RCL) polymer
model, where monomer pairs are connected randomly. We obtain asymptotic
formulas for the steady-state variance, encounter probability, the radius of
gyration, instantaneous displacement and the mean first encounter time between
any two monomers. The analytical results are confirmed by Brownian simulations.
Finally, the present results can be used to extract the minimum number of
cross-links in a chromatin region from {conformation capture} data.