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

Mathematics > Probability

arXiv:2210.00810 (math)
[Submitted on 3 Oct 2022 (v1), last revised 26 Feb 2024 (this version, v3)]

Title:Random rotor walks and i.i.d. sandpiles on Sierpinski graphs

Authors:Robin Kaiser, Ecaterina Sava-Huss
View PDF
Abstract:We prove that, on the infinite Sierpinski gasket graph SG, rotor walk with random initial configuration of rotors is recurrent. We also give a necessary condition for an i.i.d. sandpile to stabilize. In particular, we prove that an i.i.d. sandpile with expected number of chips per site greater or equal to three does not stabilize almost surely. Furthermore, the proof also applies to divisible sandpiles and shows that divisible sandpile at critical density one does not stabilize almost surely on SG.
Comments: 13 pages, 3 figures; referee's suggestions implemented; to appear in Statistics and Probability Letters (2024)
Subjects: Probability (math.PR); Combinatorics (math.CO)
MSC classes: 60J10, 60J45, 05C81
Cite as: arXiv:2210.00810 [math.PR]
  (or arXiv:2210.00810v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.2210.00810

Submission history

From: Ecaterina Sava-Huss [view email]
[v1] Mon, 3 Oct 2022 10:45:50 UTC (22 KB)
[v2] Mon, 30 Jan 2023 11:03:23 UTC (22 KB)
[v3] Mon, 26 Feb 2024 09:13:03 UTC (26 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.PR
< prev   |   next >
new | recent | 2022-10
Change to browse by:
math
math.CO

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?)