Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Nonlinear Sciences > Chaotic Dynamics

arXiv:nlin/0204056 (nlin)
[Submitted on 23 Apr 2002]

Title:Algebraic decay in hierarchical graphs

Authors:Felipe Barra, Thomas Gilbert
View PDF
Abstract: We study the algebraic decay of the survival probability in open hierarchical graphs. We present a model of a persistent random walk on a hierarchical graph and study the spectral properties of the Frobenius-Perron operator. Using a perturbative scheme, we derive the exponent of the classical algebraic decay in terms of two parameters of the model. One parameter defines the geometrical relation between the length scales on the graph, and the other relates to the probabilities for the random walker to go from one level of the hierarchy to another. The scattering resonances of the corresponding hierarchical quantum graphs are also studied. The width distribution shows the scaling behavior $P(\Gamma) \sim 1/\Gamma$.
Comments: 15 pages, 4 figures, 1 table. To appear in J. Stat. Phys
Subjects: Chaotic Dynamics (nlin.CD)
Cite as: arXiv:nlin/0204056 [nlin.CD]
  (or arXiv:nlin/0204056v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.nlin/0204056
Related DOI: https://doi.org/10.1023/A%3A1020427018179

Submission history

From: Thomas Gilbert [view email]
[v1] Tue, 23 Apr 2002 15:17:59 UTC (50 KB)
Full-text links:

Access Paper:

view license
Current browse context:
nlin.CD
< prev   |   next >
new | recent | 2002-04

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)