{"ID":2897527,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.04983","arxiv_id":"2507.04983","title":"Monitoring for a Phase Transition in a Time Series of Wigner Matrices","abstract":"We develop methodology and theory for the detection of a phase transition in a time-series of high-dimensional random matrices. In the model we study, at each time point \\( t = 1,2,\\ldots \\), we observe a deformed Wigner matrix \\( \\mathbf{M}_t \\), where the unobservable deformation represents a latent signal. This signal is detectable only in the supercritical regime, and our objective is to detect the transition to this regime in real time, as new matrix--valued observations arrive. Our approach is based on a partial sum process of extremal eigenvalues of $\\mathbf{M}_t$, and its theoretical analysis combines state-of-the-art tools from random-matrix-theory and Gaussian approximations. The resulting detector is self-normalized, which ensures appropriate scaling for convergence and a pivotal limit, without any additional parameter estimation. Simulations show excellent performance for varying dimensions. Applications to pollution monitoring and social interactions in primates illustrate the usefulness of our approach.","short_abstract":"We develop methodology and theory for the detection of a phase transition in a time-series of high-dimensional random matrices. In the model we study, at each time point \\( t = 1,2,\\ldots \\), we observe a deformed Wigner matrix \\( \\mathbf{M}_t \\), where the unobservable deformation represents a latent signal. This sign...","url_abs":"https://arxiv.org/abs/2507.04983","url_pdf":"https://arxiv.org/pdf/2507.04983v1","authors":"[\"Nina Dörnemann\",\"Piotr Kokoszka\",\"Tim Kutta\",\"Sunmin Lee\"]","published":"2025-07-07T13:25:07Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}