Delocalization of Eigenfunctions for Discrete Schrödinger Operators on Graphs

Vortrag von Andrea Ulliana

Datum: 10.12.25  Zeit: 13.30 - 14.30  Raum: Y27H28

Schrödinger operators and their localization phenomena play a central role in spectral theory and its connection to dynamical systems. In this talk, I will focus on discrete Schrödinger operators defined on large finite graphs and investigate their asymptotic behavior as the graph size tends to infinity. In joint work with A. Avila, we establish a general criterion showing that for any family of graphs without eigenvalues concentration, delocalization of eigenfunctions become asymptotically dense in the space of potentials. Along the way, I will emphasize the interplay with ergodic Schrödinger operators, where the potential is generated by an underlying topological dynamical system.