  The random greedy algorithm for finding a maximal independent set in a graph
constructs a maximal independent set by inspecting the graph's vertices in a
random order, adding the current vertex to the independent set if it is not
adjacent to any previously added vertex. In this paper, we present a general
framework for computing the asymptotic density of the random greedy independent
set for sequences of (possibly random) graphs by employing a notion of local
convergence. We use this framework to give straightforward proofs for results
on previously studied families of graphs, like paths and binomial random
graphs, and to study new ones, like random trees and sparse random planar
graphs. We conclude by analysing the random greedy algorithm more closely when
the base graph is a tree.
