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A Result of Metastability for an Infinite System of Spiking Neurons

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In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This… Click to show full abstract

In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This model has a parameter $\gamma$, corresponding to the rate of the leaking times of the neurons and, as the title says, it was proven there to present a phase transition phenomenon with respect to this $\gamma$. Here we prove that this model also exhibit a metastable behavior. By this we mean that if $\gamma$ is small enough, then the re-normalized time of extinction converges toward an exponential random variable of mean 1 as the number of neurons goes to infinity.

Keywords: metastability infinite; system spiking; result metastability; infinite system; spiking neurons

Journal Title: Journal of Statistical Physics
Year Published: 2019

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