Given the measure on random walk paths $P_0$ and a Hamiltonian $H$ the Gibbs perturbation of $H$ defined by
$$\frac{dP_{\beta,t}}{dP_0}=Z^{-1}_{\beta,t}\exp\{\beta H(x)\}$$
with
$$Z_{\beta,t}=\int \exp\{-\beta H(x)\}dP_0(x)$$
gives a new measure on paths $x$ which can be viewed as polymers.
In the case $H(x)=\int_0^t\delta_0(x_{s})ds(\int_0^t\delta_0(x_{s})dW_s)$ we say the resulting measure is concentrated on "homopolymers" ("heteropolymers") and are interested in the influence of dimension and $\beta$ on their behavior.