Since first January 2018, J. Angst, R. Imekraz, T. Letendre, M. Rossi and myself have started the project Unirandom which is founded by the Anr ( grant ANR-17-CE40-0008). This project is dedicated to the study of random nodal domains from the point of view of universality, that is to say, which properties of random nodal sets are independent of the specific choice of the underlying randomness. The project ended in june 2023.
A dedicated webpage is here: https://unirandom.univ-rennes1.fr/