Conference Agenda
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
|
Daily Overview |
| Session | |
|
Random Matrix Theory Location: 1.012 Session Chair: Nestor Parolya | |
    | |
Central limit theorems for linear eigenvalue statistics of random geometric graphs Leiden University, Netherlands, The Random geometric graphs provide a fundamental model for spatially embedded networks, yet their spectral fluctuations remain poorly understood. In this talk, I will present the first rigorous results on Gaussian fluctuations of linear eigenvalue statistics for such graphs. Specifically, we establish central limit theorems for quantities of the form $\mathrm{Tr}[\phi(A)]$, where $A$ denotes the adjacency matrix and $\phi$ belongs to a broad class of test functions, including non-polynomial functions. In the polynomial setting, we go further and prove a quantitative central limit theorem with an explicit rate of convergence to the limiting Gaussian distribution. I will also discuss extensions of these results to other canonical spatial networks, such as $k$-nearest neighbor graphs and relative neighborhood graphs. Together, these results highlight new mechanisms governing spectral fluctuations in random spatial structures and reveal a delicate interplay between geometry, local dependence, and spectral behavior. The talk is based on joint work with Christian Hirsch (Aarhus) and Kyeongsik Nam (Seoul). | |
