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 study Liouville first passage percolation metrics associated to a Gaussian free field hh
mollified by the two-dimensional heat kernel pt p_t in the bulk, and related star-scale …

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 …

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 …

We review recent progress relating to the extreme value statistics of the characteristic
polynomials of random matrices associated with the classical compact groups, and of the …

Two-pointed quantum disks with a weight parameter W> 0 are a family of finite-area random
surfaces that arise naturally in Liouville quantum gravity. In this paper we show that …

Given a planar continuum Gaussian free field h𝒰 in a domain 𝒰 with Dirichlet boundary
condition and any δ> 0, we let be a real‐valued smooth Gaussian process where is the …

In this article, we establish novel decompositions of Gaussian fields taking values in suitable
spaces of generalized functions, and then use these decompositions to prove results about …

We consider a subcritical Gaussian multiplicative chaos (GMC) measure defined on the unit
interval 0,1 and prove an exact formula for the fractional moments of the total mass of this …

Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a
partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the …