Work

Iterated Graph Systems (III): Alexander-Orbach conjecture on hierarchical lattices

Year: 2026

Type: preprint

Abstract: Can the Alexander-Orbach conjecture hold on hierarchical lattices? We construct Gromov-Hausdorff-Prokhorov scaling limits of critical percolation clusters on hierarchical lattices in the chemical metric and determine the typical spectral dimensions of the associated diffusions. These dimensions are dense in $(1,2)$; however, outside a narrow region in dimension space, we prove that the Alexander-Orbach conjecture fails on every hierarchical lattice under consideration.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.16875

Author: Neroli, Ziyu

Institution: Imperial College London

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Engineering and Physical Sciences Research Council, Division of Mathematical Sciences

Awards: Additional Funding for Mathematical Sciences: Heilbronn Institute for Mathematical Research, EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation

OpenAlex ID: W7221768100

Cites: 5

Cited by:

Related to: 10