Topological transition in disordered planar matching: combinatorial arcs expansion

Autor:	Lokhov, Andrey Y., Valba, Olga V., Nechaev, Sergei K., Tamm, Mikhail V.
Rok vydání:	2014
Předmět:	Condensed Matter - Statistical Mechanics Condensed Matter - Disordered Systems and Neural Networks Mathematics - Combinatorics
Zdroj:	J. Stat. Mech. (2014) P12004
Druh dokumentu:	Working Paper
DOI:	10.1088/1742-5468/2014/12/P12004
Popis:	In this paper, we investigate analytically the properties of the disordered Bernoulli model of planar matching. This model is characterized by a topological phase transition, yielding complete planar matching solutions only above a critical density threshold. We develop a combinatorial procedure of arcs expansion that explicitly takes into account the contribution of short arcs, and allows to obtain an accurate analytical estimation of the critical value by reducing the global constrained problem to a set of local ones. As an application to a toy representation of the RNA secondary structures, we suggest generalized models that incorporate a one-to-one correspondence between the contact matrix and the RNA-type sequence, thus giving sense to the notion of effective non-integer alphabets. Comment: 28 pages, 6 figures, published version
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1406.5537 Zobrazit plný text záznamu View this record from Arxiv