We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs in RNA secondary structures, and give convincing evidence that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation $\sqrt{5 \sqrt{5} -11}/2= 0.2123322205\dots$
翻译:我们推导了RNA二级结构中发夹结构数量与碱基对数量的期望、方差、协方差以及若干混合矩的精确渐近表达式,并提供了有力证据表明这对随机变量(发夹结构数量,碱基对数量)的中心尺度化分布在分布上收敛于相关系数为$\sqrt{5 \sqrt{5} -11}/2= 0.2123322205\dots$的双变量正态分布。