Remove the Gaussian-environment assumption

Establish the scaling-limit results for the disordered pinning model in correlated environments under the weaker assumption that the environment has a finite exponential moment, without requiring Gaussianity.

Background

The paper assumes that the correlated random environment is Gaussian, which enables the conditional Gaussian computations used in the proof, particularly those involving the decomposition and projection of the Hamiltonian. The authors note that related intermediate-disorder results for independent environments suggest that Gaussianity may be unnecessary and that a finite exponential moment could suffice.

The authors explicitly conjecture that Gaussianity can be removed, while emphasizing that the corresponding arguments would require substantially more delicate estimates because the current Gaussian computations would no longer apply directly.