Bulk universality for deformed GinUEs

Consider a random matrix of size [Formula: see text] as an additive deformation of the complex Ginibre ensemble under a deterministic matrix [Formula: see text]. Under certain assumptions on [Formula: see text], we prove that the local eigenvalue statistics in the bulk are governed by the Ginibre bulk statistics, which form a class of determinantal point process with the correlation kernel [Formula: see text] This is the continuation of the previous joint papers [D.-Z. Liu and L. Zhang, Critical edge statistics for deformed GinUEs, preprint (2023), arXiv:2311.13227v1] and [D.-Z. Liu and L. Zhang, Repeated erfc statistics for deformed GinUEs, preprint (2025), arXiv:2402.14362], which deal with the local eigenvalue statistics at the edge.