Polynomial mixing for the white-forced wave equation on the whole line

The paper proves uniqueness of the stationary measure and polynomial mixing (indeed, for any p>1) for the white-forced 1D damped nonlinear wave equation on R via a mixing-extension criterion together with a weighted Foias–Prodi estimate and weighted energy bounds (Theorem 1.1 and its consequences) . The candidate solution reaches the same result with a closely related coupling scheme but phrases the inference step through weak Harris/asymptotic coupling, rather than the paper’s specific abstract criterion. Technically, the model’s outline omits two auxiliary summability requirements present in the paper’s Assumption (A) (namely ∑|(h,ei)|‖ei‖^2 and B3 := ∑|bi|‖ei‖^2) that are used in the paper’s weighted Itô and Girsanov estimates; these should be adopted for a fully rigorous match to the paper’s framework . Aside from these minor omissions and the different abstract inference step (Harris vs mixing-extension), the skeleton of estimates—Lyapunov/weighted bounds, a weighted Foias–Prodi inequality, and a low-mode coupling via absolute continuity—aligns with the paper’s method (see Sections 2–5, incl. the construction of the mixing extension and the use of Girsanov to control the tilted law) .