Year: 2026
Type: preprint
Abstract: We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly as $\text{polylog}(m)$) to the extended semi-discrete sine kernel. As an application, we show fixed-energy universality of bulk local statistics of complex Hermitian Wigner matrices matching the covariance structure of GUE and with a finite $4+\varepsilon$ moment for $\varepsilon>0$. This application demonstrates that it is possible to obtain universality of bulk local statistics under near-optimal moment assumptions without using a Dyson Brownian motion relaxation step, which was a key ingredient in many results on this topic.
Source: arXiv (Cornell University)
Author: Himwich, Zoe
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7159690355
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