Webinar: Johannes Heiny (KTH) March 6

The first webinar of the spring 2026 will be given by Johannes Heiny (KTH).

When: Friday March 6, 11.00 – 11.45

Where: Zoom (https://kth-se.zoom.us/j/61560085260)

Titel: The Curse and Blessing of Dimensionality: A Random Matrix Perspective

Abstract: The dramatic increase and improvement of computing power and data collection devices have triggered the necessity to study and interpret the sometimes overwhelming amounts of data in an efficient and tractable way. Random matrix theory (RMT) has emerged as a powerful framework for analyzing high-dimensional data across a wide range of modern applications. As datasets grow in size and complexity, classical statistical assumptions often break down, while RMT provides asymptotic laws and spectral insights that remain stable in the high-dimensional regime. These tools enable robust estimation, anomaly detection, dimensionality reduction, and the characterization of noise versus signal in complex systems. By modeling data-dependent matrices—such as covariance, correlation, kernel, and adjacency matrices—RMT offers principled approaches for understanding their eigenvalue distributions and fluctuations. Consequently, RMT has become indispensable in fields including machine learning, finance, network science, wireless communications, and genomics, where large-scale structure and uncertainty must be navigated effectively.

In this talk, I will introduce the Marchenko–Pastur and semicircle laws, which describe the limiting eigenvalue distributions of large random matrices. After discussing the challenges posed by covariance estimation in high-dimensional settings, I will turn to the classical problem of testing independence. In this context, we will see how self-normalization can stabilize the eigenvalue distribution of large random matrices, leading to more robust statistical procedures.