Convergence of the Temporal Averages of a Metastable System of Spiking Neurons

Autor:	André, Morgan
Rok vydání:	2022
Předmět:	Mathematics - Probability Mathematical Physics 60K35 82C32 82C22
Druh dokumentu:	Working Paper
Popis:	We consider a stochastic system of spiking neurons which was previously proven to present a metastable behavior for a suitable choice of the parameter, in the sense that the time of extinction is asymptotically memory-less when the number of components in the system goes to $\infty$. In the present article we complete this work by showing that, previous to extinction, the system tends to stabilize in the sense that temporal means taken on an appropriate time scale converge in probability to some fixed value. This property is sometime called thermalization. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.12147 Zobrazit plný text záznamu View this record from Arxiv