具有外部相互作用的RNA矩阵模型及其渐近性态
RNA matrix models with external interactions and their asymptotic behaviour
摘要：
我们研究了RNA的矩阵模型，其中外部扰动作用于聚合物链的n个核苷酸。扰动的影响出现在配分函数的指数生成函数中，作为因子$(1-\frac{nα}{L})$ [其中$(1-\frac{nα}{L})$是原始项与扰动项的强度之比，L是链的长度]。数值分析了当（i）$n=L$和（ii）$n=1$时扩展矩阵模型亏格分布函数的渐近行为。在这些RNA的矩阵模型中，当$nα/L$从0增加到1时，发现在固定长度L和亏格g下的图数$a_{L, g}$的普适性从$3^{L}$变为$(3-\frac{nα}{L})^{L}$（$2^{L}$当$nα/L=1$时）和在固定长度L但独立于亏格g的图总数$\cal N$的渐近表达式，因子$\exp^{\sqrt{L}}$至$\exp^{(1-\frac{nα}{L})\sqrt{L}}$的变化（当$nα/L=1$时为$exp^{0}=1$）
英文摘要：
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 $(1-\frac{nα}{L})$ [where $α$ 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 $nα/L$ 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 $(3-\frac{nα}{L})^{L}$ ($2^{L}$ when $nα/L=1$) and the asymptotic expression of the total number of diagrams $\cal N$ at a fixed length L but independent of genus g, changes in the factor $\exp^{\sqrt{L}}$ to $\exp^{(1-\frac{nα}{L})\sqrt{L}}$ ($exp^{0}=1$ when $nα/L=1$)
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
