Pirmin Lemberger.
Large field versus small field expansions and Sobolev inequalities
(147K, LaTeX)

ABSTRACT.  We study a model for a two dimensional random interface $\phi(x)$, 
\mbox{$x\in\R^2$} described by a
massless gaussian measure perturbed by a weak potential \linebreak 
\mbox{$V(\phi)=\frac{\eps^2}{2}(\ex {-\alpha\phi}-1)^2$}. 
Such a model occurs for instance in a phenomenological
description of the wetting transition. We prove that, provided $\alpha$ is 
small enough, the two-point function decreases exponentially with a rate of 
order $m\equiv\eps\alpha$ which is just the mean field value.
The large field region problem due to the fact that $V(\phi)$ remains bounded 
when $\phi\rightarrow +\infty$ is treated by means of a large field versus 
small field expansion combined with elementary Sobolev inequalities. The 
paper is intended to be accessible to non-experts.