We give bijections between bipolar-oriented (acyclic with unique source and sink) planar
maps and certain random walks, which show that the uniformly random bipolar-oriented …

We introduce a general technique for proving estimates for certain random planar maps
which belong to the γ γ-Liouville quantum gravity (LQG) universality class for γ ∈ (0, 2) …

Counting walks with large steps in an orthant Page 1 © 2021 European Mathematical
Society Published by EMS Press. This work is licensed under a CC BY 4.0 license. J. Eur …

Abstract Let γ ∈ (0, 2) γ∈(0, 2) and let h be the random distribution on\mathbb CC which
describes a γ γ-Liouville quantum gravity (LQG) cone. Also let κ= 16/γ^ 2> 4 κ= 16/γ 2> 4 …

In this paper, we survey and discuss various surface phenomena such as prewetting,
layering and faceting for a family of two-and three-dimensional low-temperature models of …

We continue our study of the inventory accumulation introduced by Sheffield (2011), which
encodes a random planar map decorated by a collection of loops sampled from the critical …

We prove scaling limit results for the finite-volume version of the inventory accumulation
model of Sheffield (2011), which encodes a random planar map decorated by a collection of …

For a random walk killed at leaving a cone we suggest two new constructions of a positive
harmonic function. These constructions allow one to remove a quite strong extendability …

Kenyon, Miller, Sheffield, and Wilson (2015) showed how to encode a random bipolar-
oriented planar map by means of a random walk with a certain step size distribution. Using …

We consider families of non-colliding random walks above a hard wall, which are subject to
a self-potential of tilted area type. We view such ensembles as effective models for the level …