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We consider an infinite system of spiking neurons with a drift and bothexcitatory and inhibitory connections. We study conditions fornon-explosiveness and the uniqueness of the invariant measure. In particular,we examine conditions that allow this infinite interacting system to go beyondthe usual interactions of uniformly summable weights. As a result, we extendthe Galves-L\"ocherbach model beyond the restrictive uniform summability of themodel.

Interacting systems of infinite spiking neurons with weights beyond uniform summability