Monday, January 30, 2012

1109.1959 (Matthias Keller)

Absolutely continuous spectrum for multi-type Galton Watson trees    [PDF]

Matthias Keller
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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