Weil-Petersson random hyperbolic surfaces

In this paper, we aim to provide a concise introduction to the recent development of the emerging interdisciplinary field concerning random hyperbolic surfaces within the Weil-Petersson probabilistic framework. By focusing on key breakthroughs in this subject over the past decade, we delve into several significant achievements in the geometry and spectral theory of random hyperbolic surfaces. Furthermore, we propose certain open problems that offer potential directions for future research.