We investigate the multiplicative statistics of unitary random matrix ensembles under a parameter-dependent deformation of the probability measure. This deformation induces a thinning of the eigenvalues. In the past, this system was analyzed for bounded or decaying parameters, which corresponds to a finite number of particles subject to the thinning. In this work, we establish results for a growing parameter, which corresponds to the thinning of a set that blows up as the dimension increases. Our analysis proves that these statistics asymptotically converge to the lower tail of the Kardar-Parisi-Zhang (KPZ).
This presentation is based on arXiv:2511.01120.
