Two-dimensional random walk and loop factor in helix-coil transition theory of DNA

Theory of helix-coil transition in double-stranded homopolypeptides is considered. The theory develops an approach, which takes into account fundamental properties of the system (loop formation under complementary binding). Calculations are done in the framework of random walk theory. Partition function of the system is obtained in terms of arbitrary and first returns. It is shown that the loop factor of the theory has a power law behavior depending on the length of the chain.