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 show that for each γ ∈ (0, 2) γ∈(0, 2), there is a unique metric (ie, distance function)
associated with γ γ-Liouville quantum gravity (LQG). More precisely, we show that for the …

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 …

Dorn and Otto (1994) and independently Zamolodchikov and Zamolodchikov (1996)
proposed a remarkable explicit expression, the so-called-M DOZZ formula, for the three …

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 …

In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for
the density of the total mass of (subcritical) Gaussian multiplicative chaos (GMC) associated …

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on
Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context …

We demonstrate that the conformal loop ensemble (CLE) has a rich integrable structure by
establishing exact formulas for two CLE observables. The first describes the joint moments …