Bulk spacings in non-Hermitian matrix models

Random matrix eigenvalue spacings tend to show up in problems not directly related to random matrices: for instance, bumper to bumper distances of parked cars in a number of roads in central London are well represented by the so-called eigenvalue bulk spacing distribution of a suitable Hermitian matrix model. In this talk we will first survey several occurrences of these Hermitian spacing distributions and afterwards try to generalise them to non-Hermitian models. As it turns out, the theory of integrable systems, especially Painleve special function theory, plays a crucial role in this field. Based on arXiv:2212.00525, joint work with Alex Little (Bristol).