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 …

Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of
measure-endowed random surfaces. LQG is defined in terms of a real parameter γ γ, and it …

We construct a conformal welding of two Liouville quantum gravity random surfaces and
show that the interface between them is a random fractal curve called the Schramm …

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 …

Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of
measure-endowed random surfaces. LQG is defined in terms of a real parameter $\gamma …

We begin by studying inventory accumulation at a LIFO (last-in-first-out) retailer with two
products. In the simplest version, the following occur with equal probability at each time step …

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 …

We give bijections between bipolar-oriented (acyclic with unique source and sink) planar
maps and certain random walks, which show that the uniformly random bipolar-oriented …

We prove that the uniform infinite half-plane quadrangulation (UIHPQ), with either general or
simple boundary, equipped with its graph distance, its natural area measure, and the curve …

Conformal loop ensembles (CLEs) are random collections of loops in a simply connected
domain, whose laws are characterized by a natural conformal invariance property. The set of …