4 papers
On the Spectral Region of 4-Cycle Stochastic Matrices
Brando Vagenende, Brecht Verbeken, Brecht F. Verbeken +2
We study the spectrum of 4-cycle row-stochastic matrices. For real eigenvalues the spectral region is [-1,1]. For nonreal eigenvalues a+ib we derive necessary conditions in terms o…
Nonnegativity of the second largest eigenvalue of tridiagonal stochastic matrices
Brando Vagenende, Brecht Verbeken, Brecht F. Verbeken +1
The spectral study of nonnegative and more specifically stochastic matrices is an important topic in matrix theory. In this paper, we prove a conjecture, formulated by Ran and Teng…
Early Evidence of Vibe-Proving with Consumer LLMs: A Case Study on Spectral Region Characterization with ChatGPT-5.2 (Thinking)
Brecht Verbeken, Brecht F. Verbeken, Brando Vagenende +3
Large Language Models (LLMs) are increasingly used as scientific copilots, but evidence on their role in research-level mathematics remains limited, especially for workflows access…
Eigenvalue regions and realising monotone stochastic matrices
Brando Vagenende, Brecht Verbeken, Brecht F. Verbeken +1
Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regi…