For the interchange-and-contact process on Z^d, the critical infection rate lambda_c(v,p) tends to 1/(2dp) as the interchange rate v tends to infinity, for every fixed particle density p.
Spread of an infection on the zero range process.Annales de l’Institut Henri Poincaré-Probabilités et Statistiques , 56(3):1898–1928, 2020
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Contact process on interchange process
For the interchange-and-contact process on Z^d, the critical infection rate lambda_c(v,p) tends to 1/(2dp) as the interchange rate v tends to infinity, for every fixed particle density p.