69 citations · 455 across the 44 of their papers we have counts for
48 papers
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…
Non-symmetric vector dyson equations
Jiaoyang Huang, Zhonggen Su, Ruizhe Xu
We study the vector Dyson equation with parameter in the complex upper half-plane , where $\mathbf{a}\in\mathbb…
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…
Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance
Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang +2
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimizati…
Robustness Implies Generalization via Data-Dependent Generalization Bounds
Kenji Kawaguchi, Zhun Deng, Kyle Luh +1
This paper proves that robustness implies generalization via data-dependent generalization bounds. As a result, robustness and generalization are shown to be connected closely in a…
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…
Efficient Derivative-free Bayesian Inference for Large-Scale Inverse Problems
Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich +1
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This ren…
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…
Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution
Daniel Z. Huang, Jiaoyang Huang
The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where…
Improve Unscented Kalman Inversion With Low-Rank Approximation and Reduced-Order Model
Daniel Z. Huang, Jiaoyang Huang
The unscented Kalman inversion (UKI) presented in [1] is a general derivative-free approach to solving the inverse problem. UKI is particularly suitable for inverse problems where…
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…
Power Iteration for Tensor PCA
Jiaoyang Huang, Daniel Z. Huang, Qing Yang +1
In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the pow…
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…
Towards Understanding the Dynamics of the First-Order Adversaries
Zhun Deng, Hangfeng He, Jiaoyang Huang +1
An acknowledged weakness of neural networks is their vulnerability to adversarial perturbations to the inputs. To improve the robustness of these models, one of the most popular de…