Zobrazeno 1 - 10
of 213
pro vyhledávání: '"Gwynne, Ewain"'
Autor:
Borga, Jacopo, Gwynne, Ewain
Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown -- or are conjectured -- to describe the scaling limit of various natural models of random constrained permut
Externí odkaz:
http://arxiv.org/abs/2409.15494
Autor:
Hip, Andres Contreras, Gwynne, Ewain
We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we s
Externí odkaz:
http://arxiv.org/abs/2406.08674
Autor:
Bou-Rabee, Ahmed, Gwynne, Ewain
We prove that random walks on a family of tilings of d-dimensional Euclidean space, with a canonical choice of conductances, converge to Brownian motion modulo time parameterization. This class of tilings includes Delaunay triangulations (the dual of
Externí odkaz:
http://arxiv.org/abs/2405.11673
Autor:
Ang, Morris, Gwynne, Ewain
There are many deep and useful theorems relating Schramm-Loewner evolution (SLE$_\kappa$) and Liouville quantum gravity ($\gamma$-LQG) in the case when the parameters satisfy $\kappa \in \{\gamma^2, 16/\gamma^2\}$. Roughly speaking, these theorems sa
Externí odkaz:
http://arxiv.org/abs/2310.11455
We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on $\mathbb R^d$ for arbitrary $d\geq 2$. More precisely, let $\{h_n\}_{n\geq 1}$ be a suitable sequence of Gaussian random functions which
Externí odkaz:
http://arxiv.org/abs/2310.03996
Autor:
Ang, Morris, Gwynne, Ewain
Consider a critical ($\gamma=2$) Liouville quantum gravity (LQG) disk together with an independent conformal loop ensemble (CLE) with parameter $\kappa=4$. We show that the critical LQG surfaces parametrized by the regions enclosed by the CLE$_4$ loo
Externí odkaz:
http://arxiv.org/abs/2308.11835
Autor:
Ang, Morris, Gwynne, Ewain
We establish the first relationship between Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG) in the supercritical (a.k.a. strongly coupled) phase, which corresponds to central charge values $\mathbf c_{\mathrm L} \in (1,25)$ or equ
Externí odkaz:
http://arxiv.org/abs/2308.11832
The Smith embedding of a finite planar map with two marked vertices, possibly with conductances on the edges, is a way of representing the map as a tiling of a finite cylinder by rectangles. In this embedding, each edge of the planar map corresponds
Externí odkaz:
http://arxiv.org/abs/2306.02988
Let $\gamma \in (0,2)$ and let $D_h$ and $\mu_h$ denote the metric and measure associated with the unit area $\gamma$-Liouville quantum gravity (LQG) sphere. We show that the closed support of the law of $(D_h,\mu_h)$ includes all length metrics and
Externí odkaz:
http://arxiv.org/abs/2305.15588
The Brownian separable permutons are a one-parameter family -- indexed by $p\in(0,1)$ -- of universal limits of random constrained permutations. We show that for each $p\in (0,1)$, there are explicit constants $1/2 < \alpha_*(p) \leq \beta^*(p) < 1$
Externí odkaz:
http://arxiv.org/abs/2303.17030