69 citations · 455 across the 44 of their papers we have counts for
34 papers · 1 filter
Height fluctuation for Lozenge Tilings of Polygons
Jiaoyang Huang
We establish Gaussian free field fluctuations for uniformly random lozenge tilings of simply connected polygonal domains with sides whose directions cycle through the three la…
Support of Dyson Brownian Motion
Jiaoyang Huang, Shengjing Xu
We consider beta-Dyson Brownian motion, with , started from a deterministic configuration with uniformly bounded support. Let be the semicircular free-convolution flow…
Edge Rigidity of Dyson Brownian Motion with General Initial Data
Amol Aggarwal, Jiaoyang Huang
In this paper, we study the edge behavior of Dyson Brownian motion with general . Specifically, we consider the scenario where the averaged initial density near the edge, on the…
Strong Characterization for the Airy Line Ensemble
Amol Aggarwal, Jiaoyang Huang
In this paper we show that a Brownian Gibbsian line ensemble whose top curve approximates a parabola must be given by the parabolic Airy line ensemble. More specifically, we prove…
Edge Universality of Random Regular Graphs of Growing Degrees
Jiaoyang Huang, Horng-Tzer Yau
We consider the statistics of extreme eigenvalues of random -regular graphs, with for arbitrarily small . We p…
Pearcey universality at cusps of polygonal lozenge tiling
Jiaoyang Huang, Fan Yang, Lingfu Zhang
We study uniformly random lozenge tilings of general simply connected polygons. Under a technical assumption that is presumably generic with respect to polygon shapes, we show that…
Asymptotics of Generalized Bessel Functions and Weight Multiplicities via Large Deviations of Radial Dunkl Processes
Jiaoyang Huang, Colin McSwiggen
This paper studies the asymptotic behavior of several central objects in Dunkl theory as the dimension of the underlying space grows large. Our starting point is the observation th…
Edge Universality of Sparse Random Matrices
Jiaoyang Huang, Horng-Tzer Yau
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erd{\H o}s-R{é}ny…
Dynamical Loop Equation
Vadim Gorin, Jiaoyang Huang
We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Noninte…
Long Random Matrices and Tensor Unfolding
Gérard Ben Arous, Daniel Zhengyu Huang, Jiaoyang Huang
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the…
Edge Statistics for Lozenge Tilings of Polygons, II: Airy Line Ensemble
Amol Aggarwal, Jiaoyang Huang
We consider uniformly random lozenge tilings of simply connected polygons subject to a technical assumption on their limit shape. We show that the edge statistics around any point…
Edge Statistics for Lozenge Tilings of Polygons, I: Concentration of Height Function on Strip Domains
Jiaoyang Huang
In this paper we study uniformly random lozenge tilings of strip domains. Under the assumption that the limiting arctic boundary has at most one cusp, we prove a nearly optimal con…
Large Deviations Asymptotics of Rectangular Spherical Integral
Alice Guionnet, Jiaoyang Huang
In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle fo…
Spectrum of Random -regular Graphs Up to the Edge
Jiaoyang Huang, Horng-Tzer Yau
Consider the normalized adjacency matrices of random -regular graphs on vertices with fixed degree . We prove that, with probability for any…
Edge Universality for Nonintersecting Brownian Bridges
Jiaoyang Huang
In this paper we study fluctuations of extreme particles of nonintersecting Brownian bridges starting from at time and ending at $b_1\leq b_…
Height Fluctuations of Random Lozenge Tilings Through Nonintersecting Random Walks
Jiaoyang Huang
In this paper we study height fluctuations of random lozenge tilings of polygonal domains on the triangular lattice through nonintersecting Bernoulli random walks. For a large clas…
Large Deviation Principles via Spherical Integrals
Serban Belinschi, Alice Guionnet, Jiaoyang Huang
In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical…
Edge rigidity and universality of random regular graphs of intermediate degree
Roland Bauerschmidt, Jiaoyang Huang, Antti Knowles +1
For random -regular graphs on vertices with , we develop a expansion of the local eigenvalue distribution about the Kesten-McKay law up to or…
Eigenvalues for the Minors of Wigner Matrices
Jiaoyang Huang
The eigenvalues for the minors of real symmetric () and complex Hermitian () Wigner matrices form the Wigner corner process, which is a multilevel interlacing particle sy…
Dyson Brownian Motion for General and Potential at the Edge
Arka Adhikari, Jiaoyang Huang
In this paper, we compare the solutions of Dyson Brownian motion with general and potential and the associated McKean-Vlasov equation near the edge. Under suitable conditio…
Law of Large Numbers and Central Limit Theorems by Jack Generating Functions
Jiaoyang Huang
In a series of papers [22-24] by Bufetov and Gorin, Schur generating functions as the Fourier transforms on the unitary group , are introduced to study the asymptotic behavio…
Invertibility of adjacency matrices for random -regular graphs
Jiaoyang Huang
Let be a fixed integer and be the adjacency matrix of a random -regular directed or undirected graph on vertices. We show there exist constants …
Invertibility of adjacency matrices for random d-regular directed graphs
Jiaoyang Huang
Let be a fixed integer, and a prime number such that . Let be the adjacency matrix of a random -regular directed graph on vertices. We show th…
Transition from Tracy-Widom to Gaussian fluctuations of extremal eigenvalues of sparse Erdős-Rényi graphs
Jiaoyang Huang, Benjamin Landon, Horng-Tzer Yau
We consider the statistics of the extreme eigenvalues of sparse random matrices, a class of random matrices that includes the normalized adjacency matrices of the Erdős-Rényi graph…