{
  "abstract": "We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configuration. We then investigate the shape of avalanches induced by adding a particle at the origin in finite boxes of size $(2n+1)\\times(2n+1)$ around the origin. In the stationary distribution on these finite boxes, we show that avalanches reach the boundary along the vertical teeth with probability tending to $1$, while the horizontal spread is of order $\\sqrt{n}$. Finally, we establish that the single-source limit shape for abelian sandpiles on the comb lattice agrees with the corresponding limit shapes for the divisible sandpile, internal diffusion-limited aggregation (IDLA), and rotor-router aggregation models. This establishes limit shape universality on the comb lattice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21359",
  "author_total": 3,
  "authors": [
    {
      "name": "Robin Kaiser"
    },
    {
      "name": "Ecaterina Sava-Huss"
    },
    {
      "name": "Julia Überbacher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/36zdxnzq2d2v9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21359",
  "fulltext_url": null,
  "id": "36zdxnzq2d2v9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21359",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7213952950",
  "pdf_url": "https://arxiv.org/pdf/2609.21359",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/36zdxnzq2d2v9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.21359",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21359"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices",
  "title_text": "Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/36zdxnzq2d2v9",
  "venue": "arXiv",
  "versions": []
}