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

TL;DR

This paper extends the Boltzmann-Gibbs principle to the $L^p$ setting for an asymmetric Ginzburg-Landau interface model, using Littlewood-Paley-Stein inequality to obtain uniform error estimates.

Contribution

It introduces an $L^p$-based approach to the Boltzmann-Gibbs principle for a specific lattice model, with detailed error bounds independent of asymmetry strength.

Findings

Established $L^p$-Boltzmann-Gibbs principle for the model.

Derived uniform error estimates depending on system size.

Applied Littlewood-Paley-Stein inequality in this context.

Abstract

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.