Before revision:  Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we have derived the stochastic differential equation for the ground state free energy of the chain . We have considered various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale-free) and have demonstrated the existence of a topological transition from sequential to essentially embedded (nested) configurations of paired links.
After revision:  Using the optimization procedure for a special class of concave-type potentials, borrowed from optimal transport analysis, we have derived the stochastic differential equation for the ground state free energy of the chain with the planar (RNA--like) architecture of paired links. We consider various distribution functions of intervals between neighboring monomers (truncated Gaussian and scale-free) and have demonstrated the existence of a topological transition from sequential to essentially embedded (nested) configurations of paired links.