46 citations · 292 across the 35 of their papers we have counts for
5 papers · 2 filters
Almost sure multifractal spectrum of SLE
Ewain Gwynne, Jason Miller, Xin Sun
Suppose that is a Schramm-Loewner evolution (SLE) in a smoothly bounded simply connected domain and that is a conformal map from t…
On Fluctuations for Random Band Toeplitz Matrices
Yiting Li, Xin Sun
In this paper we study two one-parameter families of random band Toeplitz matrices: \[ A_n(t)=\frac{1}{\sqrt{b_n}}\Big(a_{i-j}δ_{|i-j|\le[b_nt]}\Big)_{i,j=1}^n \quad\text{and}\quad…
Equivalence of Liouville measure and Gaussian free field
Nathanaël Berestycki, Scott Sheffield, Xin Sun
Given an instance of the Gaussian free field on a planar domain and a constant , one can use various regularization procedures to make sense of the Liouville qu…
Fractional Gaussian fields: a survey
Asad Lodhia, Scott Sheffield, Xin Sun +1
We discuss a family of random fields indexed by a parameter which we call the fractional Gaussian fields, given by \[ \mathrm{FGF}_s(\mathbb{R}^d)=(-Δ)^{-s/2} W,…
Ergodicity of the Airy line ensemble
Ivan Corwin, Xin Sun
In this paper, we establish the ergodicity of the Airy line ensemble. This shows that it is the only candidate for Conjecture 3.2 in [3], regarding the classification of ergodic li…