Many mathematical models of statistical physics in two dimensions are either known or
conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions …

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

We endow the 8/3-Liouville quantum gravity sphere with a metric space structure and show
that the resulting metric measure space agrees in law with the Brownian map. Recall that a …

Uniform Infinite Planar Triangulations Page 1 Digital Object Identifier (DOI) 10.1007/s00220-003-0932-3
Commun. Math. Phys. 241, 191–213 (2003) Communications in Mathematical Physics …

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 …

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 …

R.–Nous examinons les propriétés de mosaïques de type Voronoï sur des quadrangulations
bipartites de genre arbitraire. Ceci est rendu possible par une généralisation naturelle d'une …

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 …

The main theme of these lecture notes is to analyze heat conduction on disordered media
such as fractals and percolation clusters by means of both probabilistic and analytic …