A Result of Metastability for an Infinite System of Spiking Neurons

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.

24 pages

Cited by in corpus (3)

• The Effect of Graph Connecitivity on Metastability on a Stochastic System of Spiking Neurons
• Metastability in a Stochastic System of Spiking Neurons with Leakage
• Modified log-Sobolev inequality for a compact PJMP with degenerate jumps