title: Beyond mean field theory: statistical field theory for neural networks.
abstract: Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi-Peliti-Janssen formalism, are particularly useful in this regard.
authors.affiliation: Center for Learning and Memory, University of Texas at Austin, Austin, TX, USA.
authors.forename: Michael A
authors.initials: MA
authors.lastname: Buice
authors.affiliation: Laboratory of Biological Modeling, NIDDK, NIH, Bethesda, MD, USA.
authors.forename: Carson C
authors.initials: CC
authors.lastname: Chow
keywords: Boltzmann equation; dynamics (theory); finite-size scaling; neuronal networks (theory)