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.
Keywords
Cite
@article{arxiv.1203.3248,
title = {Planar diagrams from optimization},
author = {S. K. Nechaev and A. N. Sobolevski and O. V. Valba},
journal= {arXiv preprint arXiv:1203.3248},
year = {2014}
}
Comments
10 pages, 10 figures, the proof is added. arXiv admin note: text overlap with arXiv:1102.1558