Existence and properties of connections decay rate for high temperature percolation models

DOI10.1214/22-EJP822zbMATH Open1507.60135arXiv2009.12054MaRDI QIDQ6349849

Sébastien Ott

Publication date: 25 September 2020

Abstract: We consider generic finite range percolation models on $mathbb{Z}^d$ under a high temperature 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 $mathbb{R}^d$. This result is the base input to obtain fine understanding of the high temperature phase and is usually proven using correlation inequalities (such as FKG). The present work makes no use of such model specific properties.

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

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