Improved $L^{\infty }$ bounds for eigenfunctions under random perturbations in negative curvature

Maxime Ingremeau, Martin Vogel

It has been known since the work of Avakumovíc, Hörmander and Levitan that, on any compact smooth Riemannian manifold, if $-{\Delta }_g{\psi }_{\lambda }=\lambda {\psi }_{\lambda }$, then $\|ψ_λ\|_{L^\infty} \leq C λ^{\frac…