Complex networks are key to describing the connected nature of the society that we live in.
This book, the second of two volumes, describes the local structure of random graph models …

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 …

Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with
Dirichlet energy (2 π)− 1∫ D∇ h (z)⋅∇ h (z) dz, and a constant 0≤ γ< 2. The Liouville …

We investigate unimodular random networks. Our motivations include their characterization
via reversibility of an associated random walk and their similarities to unimodular quasi …

This survey describes a general approach to a class of problems that arise in combinatorial
probability and combinatorial optimization. Formally, the method is part of weak …

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 …

Abstract 1 Introduction 1.1 General Motivation 1.2 Loop-Erased Random Walks 1.3 Iterations
of Conformal Maps and SLE 1.4 The Critical Percolation Exploration Process 1.5 Chordal …

A construction as a growth process for sampling of the uniform in-finite planar triangulation
(UIPT), defined in [AnS], is given. The construction is algorithmic in nature, and is an efficient …

We discuss scaling limits of large bipartite planar maps. If p≥ 2 is a fixed integer, we
consider, for every integer n≥ 2, a random planar map M n which is uniformly distributed …

Graphs are usually represented as geometric objects drawn in the plane, consisting of
nodes and curves connecting them. The main message of this book is that such a …