Planar diagrams from optimization

Abstract

We propose a new toy model of a heteropolymer chain capable of forming planar secondary structures typical for RNA molecules. In this model the sequential intervals between neighboring monomers along a chain are considered as quenched random variables. Using the optimization procedure for a special class of concave--type potentials, borrowed from optimal transport analysis, we derive the local difference 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 demonstrate the existence of a topological crossover from sequential to essentially embedded (nested) configurations of paired links.

10 pages, 10 figures, the proof is added. arXiv admin note: text overlap with arXiv:1102.1558

References in corpus (2)

• Local matching indicators for transport problems with concave costs
• Minimum-weight perfect matching for non-intrinsic distances on the line

Cited by in corpus (3)

• On the one dimensional Euclidean matching problem: exact solutions, correlation functions and universality
• Random Euclidean matching problems in one dimension
• The Dyck bound in the concave 1-dimensional random assignment model