# Interacting systems of infinite spiking neurons with weights beyond uniform summability

## TL;DR

This paper extends the Galves-L"ocherbach model of infinite spiking neurons to include non-uniformly summable weights, analyzing conditions for system stability and uniqueness of invariant measures.

## Contribution

It introduces a framework for infinite neuron systems with weights beyond uniform summability, broadening the applicability of existing models.

## Key findings

- Established conditions for non-explosiveness of the system.
- Proved uniqueness of the invariant measure under new conditions.
- Extended the Galves-L"ocherbach model to more general weight interactions.

## Abstract

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