In this article, we first extend the construction of random interlacements,
introduced by A.S. Sznitman in [arXiv:0704.2560], to the more general setting
of transient weighted graphs. We prove the Harris-FKG inequality for this model
and analyze some of its properties on specific classes of graphs. For the case
of non-amenable graphs, we prove that the critical value u_* for the
percolation of the vacant set is finite. We also prove that, once G satisfies
the isoperimetric inequality IS_6 (see (1.5)), u_* is positive for the product
GxZ (where we endow Z with unit weights). When the graph under consideration is
a tree, we are able to characterize the vacant cluster containing some fixed
point in terms of a Bernoulli independent percolation process. For the specific
case of regular trees, we obtain an explicit formula for the critical value
u_*.Comment: 25 pages, 2 figures, accepted for publication in the Elect. Journal
of Pro
