Surface measures and related functional inequalities on configuration spaces

Using finite difference operators, we define a notion of boundary and surface measure for configuration sets under Poisson measures. A Margulis-Russo type identity and a co-area formula are stated with applications to deviation inequalities and functional inequalities, and bounds are obtained on the associated isoperimetric constants.
Comment: A shortened version of this paper has been published in Statistics & Probability Letters 78 (2008) 2154-2164, see also the Preprint 2003-04, Universite de La Rochelle. As is, our intent is not for it to be published but to make it available since it has been referenced on various instances in the literature