RNA matrix models with external interactions and their asymptotic behaviour

Abstract

We study a matrix model of RNA in which an external perturbation acts on n nucleotides of the polymer chain. The effect of the perturbation appears in the exponential generating function of the partition function as a factor $(1-\frac{n\alpha }{L})$ [where $\alpha$ is the ratio of strengths of the original to the perturbed term and L is length of the chain]. The asymptotic behaviour of the genus distribution functions for the extended matrix model are analyzed numerically when (i) $n=L$ and (ii) $n=1$. In these matrix models of RNA, as $n\alpha /L$ is increased from 0 to 1, it is found that the universality of the number of diagrams $a_{L,g}$ at a fixed length L and genus g changes from $3^L$ to $(3-\frac{n\alpha }{L}{)}^L$ ($2^L$ when $n\alpha /L=1$) and the asymptotic expression of the total number of diagrams $\mathcal{N}$ at a fixed length L but independent of genus g, changes in the factor ${\exp }^{\sqrt{L}}$ to ${\exp }^{(1-\frac{n\alpha }{L})\sqrt{L}}$ ($ex{p}^0=1$ when $n\alpha /L=1$)

9 pages, 5 figures, 2 tables

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Cited by in corpus (2)

• Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
• Aspects géométriques et intégrables des modèles de matrices aléatoires