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A Data-Driven Approach to State Construction in Markov Models
Linde Van Gestel, Marie-Anne Guerry, Evy Rombaut
A Markov chain is a widely used stochastic process modelling random events over time. These models are built on subsets of the entire dataset, referred to as states, which are cons…
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…
Human-in-the-Loop LLM Grading for Handwritten Mathematics Assessments
Arne Vanhoyweghen, Vincent Holst, Melika Mobini +10
Providing timely and individualised feedback on handwritten student work is highly beneficial for learning but difficult to achieve at scale. This challenge has become more pressin…
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…