In this talk, we propose an analysis of a class of exploration processes on large random graphs having a fixed degree distribution, using the « constructing while exploring » approach: The graph is constructed by uniform pairing of half-edges, thus leading to a realization of the configuration model, while simultaneously exploring it.

Under general assumptions, we show how this approach allows to estimate key characteristics of the exploration process, to the large graph limit, by solving a system of ordinary differential equations in a space of measures, obtained as the hydrodynamic limits of a (properly scaled) sequence of point measure-valued continuous-time Markov chains. This procedure thus extends Wormald's differential equation method, to a space of infinite dimension.

We will focus on a particular example to illustrate this methodology: the greedy matching problem on general graphs, using a local matching criterion.