Skip to Main content Skip to Navigation
Conference papers

On the spectral dimension of random trees

Abstract : We determine the spectral dimensions of a variety of ensembles of infinite trees. Common to the ensembles considered is that sample trees have a distinguished infinite spine at whose vertices branches can be attached according to some probability distribution. In particular, we consider a family of ensembles of $\textit{combs}$, whose branches are linear chains, with spectral dimensions varying continuously between $1$ and $3/2$. We also introduce a class of ensembles of infinite trees, called $\textit{generic random trees}$, which are obtained as limits of ensembles of finite trees conditioned to have fixed size $N$, as $N \to \infty$. Among these ensembles is the so-called uniform random tree. We show that generic random trees have spectral dimension $d_s=4/3$.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 2:25:11 PM
Last modification on : Saturday, August 29, 2020 - 8:06:02 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 12:10:44 PM


Publisher files allowed on an open archive




Bergfinnur Durhuus, Thordur Jonsson, John Wheater. On the spectral dimension of random trees. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.183-192, ⟨10.46298/dmtcs.3507⟩. ⟨hal-01184712⟩



Record views


Files downloads