  A copolymer is a chain of repetitive units (monomers) that are almost
identical, but they differ in their degree of affinity for certain solvents.
This difference leads to striking phenomena when the polymer fluctuates in a
nonhomogeneous medium, for example, made of two solvents separated by an
interface. One may observe, for instance, the localization of the polymer at
the interface between the two solvents. A discrete model of such system, based
on the simple symmetric random walk on $\mathbb {Z}$, has been investigated in
[Bolthausen and den Hollander, Ann. Probab. 25 (1997), 1334-1366], notably in
the weak polymer-solvent coupling limit, where the convergence of the discrete
model toward a continuum model, based on Brownian motion, has been established.
This result is remarkable because it strongly suggests a universal feature of
copolymer models. In this work, we prove that this is indeed the case. More
precisely, we determine the weak coupling limit for a general class of discrete
copolymer models, obtaining as limits a one-parameter [$\alpha \in(0,1)$]
family of continuum models, based on $\alpha$-stable regenerative sets.
