We study conditions that allow infinite systems of interacting chains with memory of variable length to go beyond the usual Dobrushin condition. Then, we derive an analytical characterization of the invariant state based on Replica Mean Field limits. As a result we extend the Galves-L\"ocherbach model beyond the restrictive Dobrushin condition of the model.
Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets
Uniqueness of Dirichlet forms related to infinite systems of interacting Brownian motions
A continuous time stochastic model for biological neural nets
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