On the spectral dimension of random trees - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2006

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 $d_s=4/3$.
Fichier principal
Vignette du fichier
dmAG0111.pdf (219.24 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive
Loading...

Dates and versions

hal-01184712 , version 1 (17-08-2015)

Identifiers

Cite

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⟩

Collections

INSMI TDS-MACS
77 View
467 Download

Altmetric

Share

Gmail Facebook X LinkedIn More