The Pair-Replica-Mean-Field Limit for Intensity-based Neural Networks

DOI10.1137/20M1331664zbMath1465.37064arXiv2004.06246OpenAlexW3125563415MaRDI QIDQ4983526

Thibaud Taillefumier, François Baccelli

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.06246

zbMATH Keywords

neural networkpartial differential equationboundary value problemstochastic intensitymean-field dynamicsreplica model

Mathematics Subject Classification ID

Stochastic network models in operations research (90B15) Queueing theory (aspects of probability theory) (60K25) Neural networks for/in biological studies, artificial life and related topics (92B20) Markov renewal processes, semi-Markov processes (60K15) Generation, random and stochastic difference and differential equations (37H10) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (3)

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons ⋮ Replica-mean-field limits of fragmentation-interaction-aggregation processes ⋮ Metastability in a stochastic system of spiking neurons with leakage

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