9 papers
Feasibility Correction in Linear Programs
Pedro Abdalla, Roman Vershynin, Guangyi Zou
We study feasibility correction for linear programs. Suppose an initial point satisfies most of the constraints. Can it be moved into the feasible region without changing the objec…
Poisson statistics of one-dimensional random band matrices
Jiaqi Fan, Guangyi Zou
Consider an random band matrix with bandwidth with centered real Gaussian entries. We prove that, under the (almost) sharp assumption , the bul…
Total Variation Distance between Product Distributions: an Analytic Proxy
Ariel Avital, Aryeh Kontorovich, Roman Vershynin +1
We characterize, up to universal constants, the total variation distance between finite products of arbitrary probability measures by a simple formula. A theorem of Latala reduces…
On the Subgaussianity of Quantized Linear Maps: An AI-Assisted Note
Guangyi Zou, Roman Vershynin
We prove an elementary bounded-differences inequality for functions of non-isotropic Gaussian vectors. Specifically, if has bounded coordinate differences and $X\sim\mathcal N(…
Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics
Dang-Zheng Liu, Guangyi Zou
The first paper in this series introduced a \emph{short-to-long mixing} condition that captures mean-field GOE/GUE edge universality in the supercritical sparsity regime, for symme…
Edge Universality for Inhomogeneous Random Matrices
Dang-Zheng Liu, Guangyi Zou
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mix…
Revisit the Partial Coloring Method: Prefix Spencer and Sampling
Dongrun Cai, Xue Chen, Wenxuan Shu +2
As the most powerful tool in discrepancy theory, the partial coloring method has wide applications in many problems including the Beck-Fiala problem and Spencer's celebrated result…
Outliers for deformed inhomogeneous random matrices
Ruohan Geng, Dang-Zheng Liu, Guangyi Zou
Inhomogeneous random matrices with non-trivial variance profiles determined by symmetric stochastic matrices and with independent sub-Gaussian entries up to Hermitian symmetry, enc…
Edge statistics for random band matrices
Dang-Zheng Liu, Guangyi Zou
We consider Hermitian and symmetric random band matrices on the -dimensional lattice with bandwidth , focusing on local eigenvalue statistics at…