7 papers
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 \(Ï>0\),…
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 \(Ï^2\), and finite fourth mome…
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,…