A completely elementary and self-contained proof of convergence of Gaussian multiplicative
chaos is given. The argument shows further that the limiting random measure is nontrivial in …

arXiv:2006.13767v3 [math.PR] 2 Jul 2020 Page 1 arXiv:2006.13767v3 [math.PR] 2 Jul 2020
Critical Gaussian multiplicative chaos: a review Ellen Powell∗ Abstract This review-style article …

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 aim of this review-style paper is to provide a concise, self-contained and unified
presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) …

Abstract Liouville Conformal Field Theory (LCFT) on the disk describes the conformal factor
of the quantum disk, which is the natural random surface in Liouville quantum gravity with …

What is the most natural way of choosing a random surface (two-dimensional Riemannian
manifold)? If we are given a finite set 𝑋, the easiest way to choose a random element of 𝑋 is …

We prove that when suitably normalized, small enough powers of the absolute value of the
characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary …

We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal
surfaces which first appeared in the physics literature in the 1980s. Recent works have …

Let $\gamma\in (0, 2) $, let $ h $ be the planar Gaussian free field, and let $ D_h $ be the
associated $\gamma $-Liouville quantum gravity (LQG) metric. We prove that for any …