  In this article, we develop a theory for understanding the traces left by a
random walk in the vicinity of a randomly chosen reference vertex. The analysis
is related to interlacements but goes beyond previous research by showing weak
limit theorems for the vicinity around the reference vertex together with the
path segments of the random walk in this vicinity. Roughly speaking, our limit
theorem requires appropriate mixing properties for the random walk together
with a stronger variant of Benjamini-Schramm convergence for the underlying
graph model. If these assumptions are satisfied, the limiting object can be
explicitly given in terms of the Benjamini-Schramm limit of the graph model.
