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 …

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 …

The purpose of the present work is twofold. First, we develop the theory of general self-
similar growth-fragmentation processes by focusing on martingales which appear naturally …

The directed landscape is a random directed metric on the plane that arises as the scaling
limit of classical metric models in the KPZ universality class. Typical pairs of points in the …

Geodesic coalescence, or the tendency of geodesics to merge together, is a hallmark
phenomenon observed in a variety of planar random geometries involving a random …

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 …

Fix an arbitrary compact orientable surface with a boundary and consider a uniform bipartite
random quadrangulation of this surface with $ n $ faces and boundary component lengths of …

The search for a mathematical foundation for the path integral of Euclidean quantum gravity
calls for the construction of random geometry on the spacetime manifold. Following …

Recent works have shown that there is a canonical way to to assign a metric (distance
function) to a Liouville quantum gravity (LQG) surface for any parameter γ∈(0, 2). We …

Let $ h $ be the planar Gaussian free field and let $ D_h $ be a supercritical Liouville
quantum gravity (LQG) metric associated with $ h $. Such metrics arise as subsequential …