On the Euler-Poincaré Characteristic of the planar Berry's random wave: fluctuations and a perturbation study

Elena Di Bernardino, Radomyra Shevchenko, Anna Paola Todino

We prove the Central Limit Theorem for the Euler-Poincaré characteristic of Berry's random wave model in a growing domain. We also show Gaussian fluctuations for a class of Berry's…