Abstract
We consider generic finite range percolation models on under a high temperature/low density assumption (exponential decay of connection probabilities and exponential ratio weak mixing). We prove that the rate of decay of point-to-point connections exists in every directions and show that it naturally extends to a norm on . This result is the base input to obtain fine understanding of the high temperature phase (e.g. Ornstein-Zernike asymptotics for point-to-point connexions) and is usually proven using correlation inequalities (such as FKG). The present work makes no use of such model specific properties and is therefore a step towards the universality of Ornstein-Zernike asymptotics.
Funding Statement
The author thanks the university Roma Tre for its hospitality and was supported by the Swiss NSF through an early PostDoc.Mobility Grant.
Acknowledgments
Most of this work was completed while the author was a SNSF PostDoc in the university Roma Tre. The author also thanks Yvan Velenik for a careful reading of the manuscript and for useful discussions.
Citation
Sébastien Ott. "Existence and properties of connections decay rate for high temperature percolation models." Electron. J. Probab. 27 1 - 19, 2022. https://doi.org/10.1214/22-EJP822
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