A heteropolymer near a linear interface (Q1578582)

The authors consider a quenched-disordered heteropolymer modeled by a directed simple random walk \((i,S_i)\) with an interaction given by a Hamiltonian \(H_n(S)=\lambda\sum_{i=1}^n(\omega_i+h)\text{sign}(S_i)\), where \(\lambda\) and \(h\) are parameters and \(\omega_i\) are i.i.d random variables that take values \(+1\) and \(-1\). It was shown by \textit{E. Bolthausen} and \textit{F. den Hollander} [Ann. Probab. 25, No. 3, 1334-1366 (1997; Zbl 0885.60022)] that the free energy of this system exhibits a localization-delocalization phase transition at a curve in the \((\lambda,h)\)-plane. In the present paper it is shown that the free-energy localization concept is equivalent to the pathwise localization.