Fluctuations for a conservative interface model on a wall

TL;DR

This paper studies a (1+1)-dimensional interface model constrained by a wall, proving that its equilibrium fluctuations converge to a reflected SPDE that conserves the average height, using advanced stability results.

Contribution

It introduces a new analysis of interface fluctuations with conservation and reflection, applying recent stability results for Markov processes with log-concave measures.

Findings

Fluctuations converge to a reflected SPDE.

Conservation of the average height is maintained.

Utilizes recent stability results for Markov processes.

Abstract

We consider an effective interface model on a hard wall in (1+1) dimensions, with conservation of the area between the interface and the wall. We prove that the equilibrium fluctuations of the height variable converge in law to the solution of a SPDE with reflection and conservation of the space average. The proof is based on recent results obtained with L. Ambrosio and G. Savare on stability properties of Markov processes with log-concave invariant measures.