Determinantal and Gibbs structures for the other limiting dynamics

Establish analogous determinantal structures with explicit correlation kernels, together with suitable Gibbs resampling properties, for the other two limiting dynamics studied by Assiotis and Mirsajjadi (2026).

Background

The paper derives determinantal fixed-time and multitime correlation kernels, as well as a Brownian Gibbs resampling property, for the edge-scaled logarithms of squared singular values arising from multiplicative Brownian motion on the general linear group. The authors note that Assiotis and Mirsajjadi (2026) studied two additional limiting dynamics, but the present work does not extend its determinantal and Gibbsian analysis to those processes.

The unresolved task is therefore to identify explicit correlation kernels and establish appropriate Gibbs resampling properties for each of the two remaining limiting dynamics, thereby completing the corresponding structural description across the full family considered in the earlier work.