  Let $F(N,m)$ denote a random forest on a set of $N$ vertices, chosen
uniformly from all forests with $m$ edges. Let $F(N,p)$ denote the forest
obtained by conditioning the Erdos-Renyi graph $G(N,p)$ to be acyclic. We
describe scaling limits for the largest components of $F(N,p)$ and $F(N,m)$, in
the critical window $p=N^{-1}+O(N^{-4/3})$ or $m=N/2+O(N^{2/3})$. Aldous
described a scaling limit for the largest components of $G(N,p)$ within the
critical window in terms of the excursion lengths of a reflected Brownian
motion with time-dependent drift. Our scaling limit for critical random forests
is of a similar nature, but now based on a reflected diffusion whose drift
depends on space as well as on time.
