9 citations · 9 across the 10 of their papers we have counts for
10 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…
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,…
The Empirical Spectral Distribution of i.i.d. Random Matrices with Random Perturbations
Kun Chen, Zhihua Zhang
A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the…
Characterisation of matrix entropies
Frank Hansen, Zhihua Zhang
The notion of matrix entropy was introduced by Tropp and Chen with the aim of measuring the fluctuations of random matrices. It is a certain entropy functional constructed from a r…