摘要 : We consider the Laplacian on a rooted metric tree graph with branching number K >= 2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely co... 展开 We consider the Laplacian on a rooted metric tree graph with branching number K >= 2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder. 收起