There is a simple way to" glue together" a coupled pair of continuum random trees (CRTs) to
produce a topological sphere. The sphere comes equipped with a measure and a space …

We survey the theory and applications of mating-of-trees bijections for random planar maps
and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffield …

Over fourty years ago, the physicist Polyakov proposed a bold framework for string theory, in
which the problem was reduced to the study of certain" random surfaces". He further made …

Over the past few decades, two natural random surface models have emerged within
physics and mathematics. The first is Liouville quantum gravity, which has its roots in string …

We are interested in the cycles obtained by slicing at all heights random Boltzmann
triangulations with a simple boundary. We establish a functional invariance principle for the …

We study the scaling limit of the volume and perimeter of the discovered regions in the
Markovian explorations known as peeling processes for infinite random planar maps such …

We study the pioneer points of the simple random walk on the uniform infinite planar
quadrangulation (UIPQ) using an adaptation of the peeling procedure of Angel (Geom Funct …

We start by studying a peeling process on finite random planar maps with faces of arbitrary
degrees determined by a general weight sequence, which satisfies an admissibility criterion …

We prove that a uniform infinite quadrangulation of the half-plane decorated by a self-
avoiding walk (SAW) converges in the scaling limit to the metric gluing of two independent …

Pursuing the approach of Angel and Ray (Ann Probab, 2015) we introduce and study a
family of random infinite triangulations of the full-plane that satisfy a natural spatial Markov …