The arboreal gas is Bernoulli percolation conditioned on the event that each connected component is a tree. On the complete graph K_N, there is a phase transition: a subcritical phase in which all components (trees) are small, and a supercritical phase in which a giant tree exists. Unlike percolation, the supercritical phase has many mesoscopic trees of size N^{2/3} in addition to the unique giant. I will discuss a new proof of this result by comparatively soft means, as well as some conjectures that this proof suggests.
Based on joint work with Louigi Addario-Berry and Gourab Ray.