Work

Avalanches of the Abelian sandpile on the hierarchical lattice

Year: 2026

Type: preprint

Abstract: We study the Abelian sandpile model on a sequence of finite fractal graphs: the hierarchical, or Migdal--Kadanoff, lattices. Our first main result consists of matching power-law tail bounds for the avalanche and the uniform wave started at certain "pivotal" vertices. We also establish a limiting result for the pivotal reach of the avalanche and, finally, a scaling limit for the size of a uniform wave started at a vertex of high degree.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.32687

Authors: Cattani, Luca, Chiarini, Leandro, Cipriani, Alessandra

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, Fundação de Amparo à Pesquisa do Estado de São Paulo, Engineering and Physical Sciences Research Council, Hausdorff Research Institute for Mathematics

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G1600773818, Fermionic approach to height fields in the Abelian sandpile, G591746060

OpenAlex ID: W7223677600

Cites: 4

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Related to: 10