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- W2963385854 abstract "Abstract In a series of two papers, we investigate the large deviations and asymptotic behavior of stochastic models of brain neural networks with random interaction coefficients. In this first paper, we take into account the spatial structure of the brain and consider first the presence of interaction delays that depend on the distance between cells and then the Gaussian random interaction amplitude with a mean and variance that depend on the position of the neurons and scale as the inverse of the network size. We show that the empirical measure satisfies a large deviations principle with a good rate function reaching its minimum at a unique spatially extended probability measure. This result implies an averaged convergence of the empirical measure and a propagation of chaos. The limit is characterized through a complex non-Markovian implicit equation in which the network interaction term is replaced by a nonlocal Gaussian process with a mean and covariance that depend on the statistics of the solution over the whole neural field." @default.
- W2963385854 created "2019-07-30" @default.
- W2963385854 creator A5000435674 @default.
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- W2963385854 date "2018-09-01" @default.
- W2963385854 modified "2023-09-25" @default.
- W2963385854 title "Large deviations for randomly connected neural networks: I. Spatially extended systems" @default.
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- W2963385854 doi "https://doi.org/10.1017/apr.2018.42" @default.
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