The main goal of these lectures is to present some of the recent progress in the asymptotics
for large random planar maps. Recall that a planar map is simply a graph drawn on the two …

Abstract In Athreya et al.(2015) an invariance principle is stated for a class of strong Markov
processes on tree-like metric measure spaces. It is shown that if the underlying spaces …

We study the uniform random graph C_n with n vertices drawn from a subcritical class of
connected graphs. Our main result is that the rescaled graph C_n/n converges to the …

We establish uniform sub-exponential tail bounds for the width, height and maximal
outdegree of critical Bienaymé–Galton–Watson trees conditioned on having a large fixed …

We study the graph structure of large random dissections of polygons sampled according to
Boltzmann weights, which encompasses the case of uniform dissections or uniform p …

Let t be a rooted tree and nbi (t) the number of nodes in t having i children. The degree
sequence of t satisfies, where denotes the number of nodes in t. In this paper, we consider …

We are interested in the asymptotics of random trees built by linear preferential attachment,
also known in the literature as Barabási–Albert trees or plane-oriented recursive trees. We …

We establish that if a sequence of spaces equipped with resistance metrics and measures
converge with respect to the Gromov–Hausdorff-vague topology, and a certain non …

The first main result of this paper is that the law of the (rescaled) two-dimensional uniform
spanning tree is tight in a space whose elements are measured, rooted real trees …

We give a new, simple construction of the $\alpha $-stable tree for $\alpha\in (1, 2] $. We
obtain it as the closure of an increasing sequence of $\mathbb {R} $-trees inductively built by …