Asymptotic expected number of base pairs in optimal secondary structure for random RNA using the Nussinov–Jacobson energy model

Motivated by computer experiments, we study asymptotics of the expected maximum number of base pairs in secondary structures for random RNA sequences of length nn. After proving a general limit result, we provide estimates of the limit for the binary alphabet {G,C}{G,C} with thresholds k⩾0k⩾0. We prove a general theorem entailing the existence of an asymptotic limit for the mean and standard deviation of free energy per nucleotide, as computed by mfold, for random RNA of any fixed compositional frequency; higher order moment limits are additionally shown to exist.