Research

My work in discrete mathematics and linear algebra focuses on combinatorial approaches to matrix-theoretic problems. In particular, I am interested in a functional extension of the classical principal minors and diagonal similarity problem, which in its original formulation concerns pairs of matrices with equal corresponding principal minors and their relationship to diagonal similarity. More broadly, I investigate how combinatorial structures can be used to characterize such matrix equivalence problems.

Relevant Publications & Preprints:

• H. S. Mantelos, A Structural Characterization of Determinantally Equivalent Functions, 2026. arXiv:2604.03934

• H. S. Mantelos, Determinantally equivalent nonzero functions, Discrete Mathematics, Volume 349, Article 115021, 2026. https://doi.org/10.1016/j.disc.2026.115021

• H. S. Mantelos, Classification of transformations of equivalent kernels of some determinantal point processes, Research Twinning Conference on Digitalisation and Digital Transformation, Springer (Communications in Computer and Information Science), 2023. https://doi.org/10.1007/978-3-032-04731-1 

My research in probability centers on Lévy processes, Markov additive processes, and self-similar Markov processes. More recently, I have been exploring questions related to multidimensional reflected Brownian motions and stable processes. 

I am particularly interested in fluctuation theory, path decompositions, and the structural properties of stochastic processes. 

Relevant Publications & Preprints:

• A. E. Kyprianou, H. S. Mantelos, and V. Rivero, Norm-dependent Lamperti-type MAP representations of stable processes and Brownian motions in the orthant, 2025. arXiv:2506.22020