Absolutely continuous spectrum for multi-type Galton Watson trees
Mathematical Physics
2015-05-30 v2 math.MP
Probability
Spectral Theory
Abstract
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.
Cite
@article{arxiv.1109.1959,
title = {Absolutely continuous spectrum for multi-type Galton Watson trees},
author = {Matthias Keller},
journal= {arXiv preprint arXiv:1109.1959},
year = {2015}
}
Comments
to appear in Annales Henri Poincar\'e