Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 52 min ago
Peer-reviewedCC BYComputational & applied mathematics

On the structure of the sandpile identity element on Sierpiński gasket graphs.

  • Robin Kaiser1
  • Ecaterina Sava-Huss2
  • Julia Überbacher2
  1. 1Departement of Mathematics, CIT, Technische Universität München, Boltzmannstr. 3, 85748 Garching bei München, Germany.
  2. 2Universität Innsbruck, Institut für Mathematik, Technikerstraße 13, 6020 Innsbruck, Austria.
Read full textPDFDOICite

Abstract

We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpiński gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpiński gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs.

Related

  1. Dirac measures can be quantum limits on the Sierpinski gasket
    Patricia Alonso Ruiz, Nikolay Tzvetkov
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  2. Generalization of Navascués' α-fractal operator on lifted Sierpiński gasket
    Gurubachan, S. Verma, V. V. M. S. Chandramouli
    arXivPreprintCC BY 4.0Full textDynamical systemsarXiv
  3. Hydrodynamic and Dynamical Phi^4 Limits of Ising-Kac Models with Diffusion-Based Interactions on the Sierpiński Gasket
    Hongyi Chen, Seoyeon Yang
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv
  4. A dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations
    Yi Zhang
    arXivPreprintarXiv licenceFull textMathematical physicsNumerical analysis & scientific computingarXiv
  5. A Structure-Preserving Symmetric Galerkin Boundary Element Method for Anisotropic Multi-phase Mullins-Sekerka Flow
    Tokuhiro Eto
    arXivPreprintCC BY-NC-ND 4.0Full textNumerical analysis & scientific computingarXiv

Cite

BibTeXRIS
BibTeX
@article{kaiser2026structure,
  title = {{On the structure of the sandpile identity element on Sierpiński gasket graphs.}},
  author = {Robin Kaiser and Ecaterina Sava-Huss and Julia Überbacher},
  journal = {Computational \& applied mathematics},
  year = {2026},
  month = oct,
  doi = {10.1007/s40314-026-03928-6},
  url = {https://europepmc.org/article/MED/42892848},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - On the structure of the sandpile identity element on Sierpiński gasket graphs.
AU  - Robin Kaiser
AU  - Ecaterina Sava-Huss
AU  - Julia Überbacher
PY  - 2026
DA  - 2026/10/16
JO  - Computational & applied mathematics
DO  - 10.1007/s40314-026-03928-6
UR  - https://europepmc.org/article/MED/42892848
AB  - We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpiński gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpiński gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs.
SN  - 1807-0302
ER  -