Trap models on convergent sequences of resistance networks converge and exhibit aging; with local-structure convergence they also exhibit sub-aging, covering Sierpinski gaskets, critical Galton-Watson trees, and critical Erdos-Renyi graphs.
Aldous, The continuum random tree
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Aging and sub-aging for Bouchaud trap models on resistance metric spaces
Trap models on convergent sequences of resistance networks converge and exhibit aging; with local-structure convergence they also exhibit sub-aging, covering Sierpinski gaskets, critical Galton-Watson trees, and critical Erdos-Renyi graphs.