9 papers
Fourth-Moment Strong Universality for Finite-Type Transpose-Correlated Random Matrices
Yanjin Xiang, Zhihua Zhang
We prove a strong-universality theorem at the exact fourth-moment threshold for finite families of non-Hermitian random matrices assembled from independent unordered-pair vector at…
Poincaré's Inequality on Sliding-Window Occupation Count Kernels and the Optimal Normalized Spectral-Gap Constant
Yanjin Xiang, Zhihua Zhang
Let be an irreducible reversible Markov kernel on an -state space , and denote its right spectral gap by $\Gap(P) =1-λ_2(P)$. From a stationary trajectory, let be t…
Conditionally Resampled Sliding-Window Count Kernels: Spectral-Gap Bounds and Poincaré Inequalities
Yanjin Xiang, Yuchen Xin, Zhihua Zhang
We study the conditionally resampled sliding-window count kernel associated with the empirical counts of length- windows from a stationary finite-state reversible Markov chain.…
Strong Convergence for a General Class of Random Matrix Models
Yanjin Xiang, Zhihua Zhang
Let \(X_{1,n},\ldots,X_{d,n}\) be \(n\times n\) random matrices built from independent i.i.d. entry arrays, with centered entries, normalized by \(n^{-1/2}\). We prove that, if eve…
Layerwise Terminal Discrepancy in Chen's Reverse-Heat Coupling on the Boolean Cube
Yanjin Xiang, Zhihua Zhang
Recently, Chen \cite{Chen2026} proved that Talagrand's Boolean convolution conjecture holds up to the dimension-free factor \((\log\logη)^{3/2}\), namely for every fixed \(τ>0\), \…
Universality for Products of Random Matrices with i.i.d. Entries and the Fuss--Catalan Number
Yanjin Xiang, Kun Chen, Zhihua Zhang
Let \((w_{ij})_{i,j\ge1}\) be a single infinite array of independent identically distributed real- or complex-valued entries of mean zero, variance \(σ^2\), and finite fourth momen…
Finite-Iteration Local Dynamics and Warm Starts for Alternating Power Iteration in Spiked Tensor PCA
Yanjin Xiang, Zhihua Zhang
We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is indepen…
UniMatSim: A High-Throughput Materials Simulation Automation Framework Based on Universal Machine Learning Potentials
Yanjin Xiang, Yihan Nie, Yunzhi Gao +2
Universal machine learning interatomic potentials (UMLIPs) offer accuracy close to first-principles calculations at a fraction of the cost, showing significant potential for large-…
Universality of General Spiked Tensor Models
Yanjin Xiang, Zhihua Zhang
We study asymmetric rank-one spiked tensor models in the high-dimensional regime, where the noise entries are independent and identically distributed with zero mean, unit variance,…