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Hierarchical connectivity sets the upper critical dimension of neural avalanches

  • W. A. Zúñiga-Galindo
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Abstract

Neural avalanches with size exponent 3/2 are usually explained by mean-field critical branching, which for short-range coupling requires dimension N≥4. We show that hierarchical connectivity removes this constraint. In a p-adic version of the Buice--Cowan field theory, a coupling that decays by p−(N+σ) per hierarchical level selects the Taibleson--Vladimirov operator, and the critical theory is ultrametric directed percolation with upper critical dimension Nc=2σ. Exact simulations on a tree give τS=3/2 for σ≤ N/2, decreasing continuously for σ>N/2.

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Cite

BibTeXRIS
BibTeX
@misc{zunigagalindo2026hierarchical,
  title = {{Hierarchical connectivity sets the upper critical dimension of neural avalanches}},
  author = {W. A. Zúñiga-Galindo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36404},
  eprint = {2610.36404},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36404},
}
RIS
TY  - UNPB
TI  - Hierarchical connectivity sets the upper critical dimension of neural avalanches
AU  - W. A. Zúñiga-Galindo
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.36404
UR  - https://arxiv.org/abs/2610.36404
AB  - Neural avalanches with size exponent 3/2 are usually explained by mean-field critical branching, which for short-range coupling requires dimension N≥4. We show that hierarchical connectivity removes this constraint. In a p-adic version of the Buice--Cowan field theory, a coupling that decays by p^−(N+σ) per hierarchical level selects the Taibleson--Vladimirov operator, and the critical theory is ultrametric directed percolation with upper critical dimension N_c=2σ. Exact simulations on a tree give τ_S=3/2 for σ≤ N/2, decreasing continuously for σ>N/2.
ER  -