  In this paper, we consider the random plane forest uniformly drawn from all
possible plane forests with a given degree sequence. Under suitable conditions
on the degree sequences, we consider the limit of a sequence of such forests
with the number of vertices tends to infinity in terms of
Gromov-Hausdorff-Prokhorov topology. This work falls into the general framework
of showing convergence of random combinatorial structures to certain
Gromov-Hausdorff scaling limits, described in terms of the Brownian Continuum
Random Tree, pioneered by the work of Aldous. In fact we identify the limiting
random object as a sequence of random real trees encoded by excursions of some
first passage bridges reflected at minimum. We establish such convergence by
studying the associated Lukasiewicz walk of the degree sequences. In
particular, our work is closely related to and uses the results from the recent
work of Broutin and Marckert on scaling limit of random trees with prescribed
degree sequences, and the work of Addario-Berry on tail bounds of the height of
a random tree with prescribed degree sequence.
