Freezing transition of the random bond RNA model: Statistical properties of the pairing weights

To characterize the pairing specificity of RNA secondary structures as a function of temperature, we analyze the statistics of the pairing weights as follows: for each base (i) of the sequence of length N , we consider the (N-1) pairing weights w{i}(j) with the other bases (j not equal i) of the sequence. We numerically compute the probability distributions P1(w) of the maximal weight w[{i}{max}=max{j}[w{i}(j)] , the probability distribution Pi(Y(2)) of the parameter Y2(i)= summation operator{j}w{i}{2}(j) , as well as the average values of the moments Y{k}(i)= summation operator_{j}w_{i}{k}(j) . We find that there are two important temperatures T_{c}T_{gap} , the distribution P1(w) vanishes at some value w{0}(T)<1 , and accordingly the moments Y{k}(i) decay exponentially as [w{0}(T)]{k} in k . For T