Absolutely continuous spectrum for multi-type Galton Watson trees

Details Absolutely continuous spectrum for multi-type Galton Watson trees Absolutely continuous spectrum for multi-type Galton Watson trees

2011-09-09

arxiv.org/abs/1109.1959v2

Physics

Mathematical Physics

to appear in Annales Henri Poincar\'e

Scientific paper

We consider multi-type Galton Watson trees that are close to a tree of finite
cone type in distribution. Moreover, we impose that each vertex has at least
one forward neighbor. Then, we show that the spectrum of the Laplace operator
exhibits almost surely a purely absolutely continuous component which is
included in the absolutely continuous spectrum of the tree of finite cone type.

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