On a toy network of neurons interacting through their dendrites
DOI10.1214/19-AIHP993zbMath1434.60289arXiv1802.04118MaRDI QIDQ2179621
Nicolas Fournier, Romain Veltz, Etienne Tanré
Publication date: 13 May 2020
Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.04118
propagation of chaosmean-field limitnonlinear stochastic differential equationslongest increasing subsequenceUlam's problembiological neural networks
Neural biology (92C20) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Jump processes on discrete state spaces (60J74)
Cites Work
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- Clarification and complement to ``Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons
- Limit theorems for infinite-dimensional piecewise deterministic Markov processes. Applications to stochastic excitable membrane models
- On a toy model of interacting neurons
- Transition from Gaussian to non-Gaussian fluctuations for mean-field diffusions in spatial interaction
- Quenched limits and fluctuations of the empirical measure for plane rotators in random media.
- Mean field limit for disordered diffusions with singular interactions
- A variational problem for random Young tableaux
- From Hammersley's lines to Hammersley's trees
- Mean-field limit of generalized Hawkes processes
- Dendritic sodium spikes endow neurons with inverse firing rate response to correlated synaptic activity
- Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels
- Hammersley's process with sources and sinks
- Limiting curves for i.i.d. records
- Hammersley's interacting particle process and longest increasing subsequences
- Analysis of nonlinear noisy integrate \& fire neuron models: blow-up and steady states
- Hydrodynamic limit for interacting neurons
- Particle systems with a singular mean-field self-excitation. Application to neuronal networks
- Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
- Multi-class oscillating systems of interacting neurons
- Fluid limit theorems for stochastic hybrid systems with application to neuron models
- Mean-Field Limit of a Stochastic Particle System Smoothly Interacting Through Threshold Hitting-Times and Applications to Neural Networks with Dendritic Component
- Qualitative properties of solutions for the noisy integrate and fire model in computational neuroscience
- Microscopic approach of a time elapsed neural model
- The Longest Chain Among Random Points in Euclidean Space
- A Hamilton--Jacobi Equation for the Continuum Limit of Nondominated Sorting
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