5 papers
Cellular Maximal-Density Factoring: Joint Shadings, Stable Refinements, and a Conditional Kakeya Application
Zhixu Hua, Xiufan Yang
Maximal-density factoring must often make one parent object carry several forms of information at once: child mass, two multiplicity levels, a density estimate, and the ability to…
Profile-Stable Buffered Multiplicity Factoring in Four Dimensions
Zhixu Hua, Xinshun Yao, Xiufan Yang
Multiplicity factoring is usually formulated for child families at comparable scales. For children of mixed geometry, thickening at the shortest parent scale produces nonuniform in…
Simple and distinct zeros in a prime-modulus Dirichlet family from near-microscopic to polylogarithmic heights
Zhixu Hua, Xiufan Yang
Fix \(η>0\) and \(A_0>0\). Let \(q\) tend to infinity through odd primes, put \(Q=\log q\), and let \(T=T(q)\) satisfy \[ \frac{(\log Q)^{1+η}}{Q}\le T\le Q^{A_0}. \] Set \(I=(T,2T…
One-Sided Product-Scale Upper Bounds for Nested Complex Wishart Extremes
Xiufan Yang
I study the largest eigenvalue \(Λ_j\) of \(X^{(j)}(X^{(j)})^*\), where \(X^{(j)}\) is the \(M_j\times j\) northwest rectangle of one infinite complex Gaussian array. For two upper…
Extreme least singular values of random row submatrices with bounded-density subgaussian entries
Xiufan Yang, Shu Wen, Yitzchak Shmalo
Let be a centered real subgaussian random variable with positive variance and a bounded Lebesgue density, and let have independent entries dist…