On monotonicity and couplings of random currents and the loop-O(1)-model
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Using recent couplings, we provide counterexamples to monotonicity properties of percolation models related to graphical representations of the Ising model. We further prove a new coupling of the double random current model to the loop-O(1)-model.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Alea |
| Vol/bind | 19 |
| Udgave nummer | 1 |
| Sider (fra-til) | 151-161 |
| ISSN | 1980-0436 |
| DOI | |
| Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
Received by the editors July 10th, 2020; accepted June 2nd, 2021. 2010 Mathematics Subject Classification. 82B20, 82B43, 60K35. Key words and phrases. Ising model, random currents, Eulerian percolation, percolation with degree constraints. The author has been supported by the Swiss European Mobility Exchange program as well as the Villum Foundation for support through the QMATH center of Excellence(Grant No. 10059) and the Villum Young Investigator (Grant No. 25452) programs.
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© 2022. Alea (Rio de Janeiro). All rights reserved.
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