A result of metastability for an infinite system of spiking neurons

DOI10.1007/s10955-019-02402-4zbMath1439.92048arXiv1905.07053OpenAlexW3090953025WikidataQ98799544 ScholiaQ98799544MaRDI QIDQ2283156

Morgan André

Publication date: 30 December 2019

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07053

zbMATH Keywords

metastabilityinteracting particle systemssystems of spiking neurons

Mathematics Subject Classification ID

Neural biology (92C20) Neural networks for/in biological studies, artificial life and related topics (92B20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (7)

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons ⋮ A numerical study of the time of extinction in a class of systems of spiking neurons ⋮ An interacting neuronal network with inhibition: theoretical analysis and perfect simulation ⋮ Convergence of the temporal averages of a metastable system of spiking neurons ⋮ Modified log-Sobolev inequality for a compact pure jump Markov process with degenerate jumps ⋮ Metastability for systems of interacting neurons ⋮ Metastability in a stochastic system of spiking neurons with leakage

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Infinite systems of interacting chains with memory of variable length -- a stochastic model for biological neural nets
• Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility
• Metastable behavior of stochastic dynamics: A pathwise approach
• Metastability for the contact process
• Maximum likelihood analysis of spike trains of interacting nerve cells
• An introduction to infinite particle systems
• The basic contact processes
• On a class of set-valued Markov processes
• Additive set-valued Markov processes and graphical methods
• Rigorous treatment of metastable states in the van der Waals-Maxwell theory
• Phase transition for infinite systems of spiking neurons
• Large Deviations and Metastability
• [https://portal.mardi4nfdi.de/wiki/Publication:4153440 Une classe de syst�mes de particules stable par association]
• A Metastable Result for the Finite Multidimensional Contact Process
• Markovian Interaction Processes with Finite Range Interactions
• Probability

This page was built for publication: A result of metastability for an infinite system of spiking neurons