$L^p$-Boltzmann-Gibbs principle via Littlewood-Paley-Stein inequality

In this paper, we establish the Boltzmann-Gibbs principle in the $L^p$ sense by applying the Littlewood-Paley-Stein inequality. Our model is an asymmetric Ginzburg-Landau interface model on a one-dimensional periodic lattice. Assuming convexity of the potential,we derive detailed error estimates, particularly their dependence on the size of the system and the size of the region on which the sample average is taken. Notably, the estimates are uniform in the strength of the asymmetry.