A0681
Title: Monitoring for a phase transition in a time series of Wigner matrices
Authors: Nina Doernemann - Aarhus University (Denmark) [presenting]
Tim Kutta - Aarhus University (Denmark)
Piotr Kokoszka - Colorado State University (USA)
Sunmin Lee - Colorado State University (United States)
Abstract: Methodology and theory are developed for the detection of a phase transition in a time series of high-dimensional random matrices. In the model studied, at each time point $\( t = 1,2,\ldots \)$, a deformed Wigner matrix $\( \mathbf{M}_t \)$ is observed, where the unobservable deformation represents a latent signal. This signal is detectable only in the supercritical regime, and the objective is to detect the transition to this regime in real time, as new matrix-valued observations arrive. The 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 the approach.
