Open Access
2024 An ergodic and isotropic zero-conductance model with arbitrarily strong local connectivity
Martin Heida, Benedikt Jahnel, Anh Duc Vu
Author Affiliations +
Electron. Commun. Probab. 29: 1-13 (2024). DOI: 10.1214/24-ECP633

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

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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

Information

Received: 11 March 2024; Accepted: 19 September 2024; Published: 2024
First available in Project Euclid: 13 October 2024

arXiv: 2403.06785
Digital Object Identifier: 10.1214/24-ECP633

Subjects:
Primary: 60K35 , 60K37
Secondary: 60G55 , 90B18

Keywords: conductivity , homogenisation , percolation , randomly stretched lattice

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