Frederic Klopp, Konstantin Pankrashkin
Localization on quantum graphs with random vertex couplings
(82K, latex)

ABSTRACT.  We consider Schroedinger operators on a class of periodic quantum 
 graphs with randomly distributed Kirchhoff coupling constants at all 
 vertices. Using the technique of self-adjoint extensions we obtain 
 conditions for localization on quantum graphs in terms of finite 
 volume criteria for some energy-dependent discrete Hamiltonians. 
 These conditions hold in the strong disorder limit and at the 
 spectral edges.