Statistical Physics and Interdisciplinary Applications

In my report I will show that the secondary structures of random
heteropolymers undergo a topological transition. Namely, for c less than the critical value the fraction of "active'' nucleotides (which form the base pairs) tends to 1 as the length of the chain goes to infinity, signaling the formation of a virtually "perfect'' secondary structure without gaps. In turn,
for c > c_{cr} always a non-perfect structure with gaps is formed. It was proved mathematically that 2 < c_{cr} < 3; our current research deals with determination a value of transition point; it directly connects with developing new methods to generate random sequences with "effectively" non integer alphabet.
Our previous results have shown that transition point is very close to alphabet used by Nature in real RNAs. Such a critical behavior can point to some statistical exclusivity of natural alphabet.