Estimates on path delocalization for copolymers at selective interfaces

Abstract

Starting from the simple symmetric random walk {Sn}n, we introduce a new process whose path measure is weighted by a factor exp factor $\exp (\lambda\sum^N_{n=1}(\omega_n+h){\rm sign},(S_n))$, with α,h≥0, {Wn}n a typical realization of an IID process and N a positive integer. We are looking for results in the large N limit. This factor favors Sn>0 if Wn+h>0 and Sn<0 if Wn+h<0. The process can be interpreted as a model for a random heterogeneous polymer in the proximity of an interface separating two selective solvents. It has been sh Show more