Absolutely continuous spectrum of random quantum trees

Simone Warzel Princeton University, USA

We consider the Laplacian on a rooted metric tree graph with branching number K > 1 and random edge lengths given by independent and identically distributed variables. Our main result is the stability of the absolutely continuous spectrum for small randomness. (This is joint work with M. Aizenman, R. Sims, and U. Smilansky.)