  This article considers some classes of models dealing with the dynamics of
discrete curves subjected to stochastic deformations. It turns out that the
problems of interest can be set in terms of interacting exclusion processes,
the ultimate goal being to derive hydrodynamic limits after proper scalings. A
seemingly new method is proposed, which relies on the analysis of specific
partial differential operators, involving variational calculus and functional
integration: indeed, the variables are the values of some functions at given
points, the number of which tends to become infinite, which requires the
construction of \emph{generalized measures}. Starting from a detailed analysis
of the \textsc{asep} system on the torus Z/N/Z, we claim that the arguments a
priori work in higher dimensions (ABC, multi-type exclusion processes, etc),
leading to sytems of coupled partial differential equations of Burgers' type.
