Bulk universality for deformed GinUEs

For the deformed complex Ginibre ensemble with a mean normal matrix, under certain assumptions on the mean matrix we prove that the same bulk statistics holds as in the complex Ginibre matrix bulk. This is the continuation of the previous joint papers Critical edge statistics for deformed GinUEs Preprint arXiv: 2311.13227v1'' and Repeated erfc statistics for deformed GinUEs Preprint arXiv: 2402.14362’', which deal with local eigenvalue statistics at the edge.