Edward Zeng

activity

20222026

collaborators

3 papers

math.PR2026

Spectra of Random Polynomial Matrices: the Petaloid Law

Rikhav Shah, Edward Zeng

We study the distribution of the zeros of $det P_{N} (z)$ where $P_{N} (z)$ is a random monic polynomial matrix, i.e., $P_{N} (z) = z^{d} I - \sum_{j = 0}^{d - 1} A_{j, N} z^{j}$ for possibly coupled rand…

math.PR2024

Sparse Pseudospectral Shattering

Rikhav Shah, Nikhil Srivastava, Edward Zeng

The eigenvalues and eigenvectors of nonnormal matrices can be unstable under perturbations of their entries. This renders an obstacle to the analysis of numerical algorithms for no…

math.PR2022

Invertibility of Sparse Complex Gaussian Matrices

Edward Zeng

Let $σ_{n} (\cdot)$ denote the least singular value of a $n \times n$ matrix. It is well-known that $P [σ_{n} (A) \leq ε] \leq ε n$ if $A$ is drawn from the rea…