Abstract
We exhibit a percolating ergodic and isotropic lattice model in all but at least two dimensions that has zero effective conductivity in all spatial directions and for all non-trivial choices of the connectivity parameter. The model is based on the so-called randomly stretched lattice where we additionally elongate layers containing few open edges.
Funding Statement
BJ and ADV received support by the Leibniz Association within the Leibniz Junior Research Group on Probabilistic Methods for Dynamic Communication Networks as part of the Leibniz Competition (grant no.\ J105/2020). MH was funded by DFG through SPP2256 project HE 8716/1-1 project ID: 441154659.
Acknowledgments
We would like to thank Sebastian Andres, Marek Biskup and Alessandra Faggionato for inspiring discussions.
Citation
Martin Heida. Benedikt Jahnel. Anh Duc Vu. "An ergodic and isotropic zero-conductance model with arbitrarily strong local connectivity." Electron. Commun. Probab. 29 1 - 13, 2024. https://doi.org/10.1214/24-ECP633
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