S. Amari, Dynamics of pattern formation in lateral-inhibition type neural fields, Biological Cybernetics, vol.13, issue.2, pp.77-87, 1977.
DOI : 10.1007/BF00337259

B. Bruno, P. E. Averbeck, A. Latham, and . Pouget, Neural correlations , population coding and computation, Nature reviews. Neuroscience, vol.7, issue.5, pp.358-366, 2006.

J. Baladron, D. Fasoli, O. Faugeras, and J. Touboul, Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons, The Journal of Mathematical Neuroscience, vol.2, issue.1, p.2012
DOI : 10.1186/2190-8567-2-10

URL : https://hal.archives-ouvertes.fr/inserm-00732288

R. John, N. C. Baxter, and . Jain, An approximation condition for large deviations and some applications, Convergence in Ergodic Theory and Probability. Ohio State University Mathematical Research Institute Publications, 1993.

G. Ben-arous and A. Guionnet, Large deviations for langevin spin glass dynamics. Probability Theory and Related Fields, pp.455-509, 1995.

P. C. Bressloff, Stochastic Neural Field Theory and the System-Size Expansion, SIAM Journal on Applied Mathematics, vol.70, issue.5, pp.1488-1521, 2009.
DOI : 10.1137/090756971

P. C. Bressloff, Spatiotemporal dynamics of continuum neural fields, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.3, p.45, 2012.
DOI : 10.1088/1751-8113/45/3/033001

P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, What Geometric Visual Hallucinations Tell Us about the Visual Cortex, Neural Computation, vol.222, issue.8, pp.473-491, 2002.
DOI : 10.1007/BF00288786

N. Brunel and D. Hansel, How Noise Affects the Synchronization Properties of Recurrent Networks of Inhibitory Neurons, Neural Computation, vol.16, issue.5, 2006.
DOI : 10.1023/A:1008841325921

URL : https://hal.archives-ouvertes.fr/hal-00173760

W. Bryc and A. Dembo, Large deviations and strong mixing, Annales de l'IHP Probabilités et statistiques, pp.549-569, 1996.

A. Budhiraja, P. Dupuis, and M. Fischer, Large deviation properties of weakly interacting processes via weak convergence methods, The Annals of Probability, vol.40, issue.1, pp.74-102, 2012.
DOI : 10.1214/10-AOP616

M. A. Buice, J. D. Cowan, and C. C. Chow, Systematic Fluctuation Expansion for Neural Network Activity Equations, Neural Computation, vol.13, issue.1, pp.377-426, 2010.
DOI : 10.1093/acprof:oso/9780198509233.001.0001

T. Chiyonobu and S. Kusuoka, The large deviation principle for hypermixing processes. Probability Theory and Related Fields, pp.627-649, 1988.

J. Cox, K. Fleischmann, and A. Greven, Comparison of interacting diffusions and an application to their ergodic theory. Probability Theory and Related Fields, pp.513-528, 1996.

D. Dawson and J. Gartner, Large deviations from the mckeanvlasov limit for weakly interacting diffusions, Stochastics, vol.20, 1987.

A. Dembo and O. Zeitouni, Large deviations techniques, 1997.

J. D. Deuschel, D. W. Stroock, and H. Zessin, Microcanonical distributions for lattice gases, Communications in Mathematical Physics, vol.77, issue.1, 1991.
DOI : 10.1007/BF02102730

J. Deuschel and D. W. Stroock, Large Deviations, Pure and Applied Mathematics, vol.137, 1989.
DOI : 10.1090/chel/342

M. D. Donsker and S. R. Varadhan, Asymptotic evaluation of certain markov process expectations for large time. IV, Communications on Pure and Applied Mathematics, vol.58, issue.2, pp.183-212, 1983.
DOI : 10.1002/cpa.3160360204

M. D. Donsker and S. R. Varadhan, Large deviations for stationary Gaussian processes, Communications in Mathematical Physics, vol.36, issue.1-2, pp.187-210, 1985.
DOI : 10.1007/BF01206186

P. Doukhan, Mixing: Properties and Examples, 1994.

G. Ermentrout and J. D. Cowan, Temporal oscillations in neuronal nets, Journal of Mathematical Biology, vol.13, issue.3, pp.265-280, 1979.
DOI : 10.1007/BF00275728

G. Ermentrout and J. Mcleod, Synopsis, Proceedings, pp.461-478, 1993.
DOI : 10.1016/0362-546X(78)90015-9

D. Fasoli, Attacking the Brain with Neuroscience: Mean-Field Theory, Finite Size Effects and Encoding Capability of Stochastic Neural Networks, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00850289

O. Faugeras and J. Maclaurin, A large deviation principle and an analytical expression of the rate function for a discrete stationary gaussian process, 2013.

G. Faye, Existence and Stability of Traveling Pulses in a Neural Field Equation with Synaptic Depression, SIAM Journal on Applied Dynamical Systems, vol.12, issue.4, 2013.
DOI : 10.1137/130913092

M. Fischer, On the form of the large deviation rate function for the empirical measures of weakly interacting systems, Bernoulli, vol.20, issue.4, 2012.
DOI : 10.3150/13-BEJ540

M. Galtier, A mathematical approach to unsupervised learning in recurrent neural networks, 2011.
URL : https://hal.archives-ouvertes.fr/pastel-00667368

M. A. Geise, Neural Field Theory for Motion Perception, 1999.
DOI : 10.1007/978-1-4615-5581-0

W. Gerstner and W. Kistler, Spiking Neuron Models, 2002.

W. Gerstner and W. M. Kistler, Mathematical formulations of Hebbian learning, Biological Cybernetics, vol.87, issue.5-6, pp.404-415, 2002.
DOI : 10.1007/s00422-002-0353-y

G. Giacomin and P. Luçon, Coherence Stability and Effect of Random Natural Frequencies in Populations of Coupled Oscillators, Journal of Dynamics and Differential Equations, vol.63, issue.2, 2011.
DOI : 10.1007/s10884-014-9370-5

URL : https://hal.archives-ouvertes.fr/hal-01018542

I. Ginzburg and H. Sompolinsky, Theory of correlations in stochastic neural networks, Physical Review E, vol.50, issue.4, 1994.
DOI : 10.1103/PhysRevE.50.3171

A. Greven and F. D. Hollander, Phase transitions for the long-time behavior of interacting diffusions. The Annals of Probability, 2007.

H. Haken, Information and Self-Organization, 2006.

D. Hansel and H. Sompolinsky, Methods in Neuronal Modeling, From Ions to Networks, chapter Modeling Feature Selectivity in Lo-cal Cortical Circuits, 1998.

Z. P. Kilpatrick and P. C. Bressloff, Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network, Physica D: Nonlinear Phenomena, vol.239, issue.9, pp.547-560, 2010.
DOI : 10.1016/j.physd.2009.06.003

M. Thomas and . Liggett, Interacting Particle Systems, 2005.

E. Luçon, Quenched limits and fluctuations of the empirical measure for plane rotators in random media, Electronic Journal of Probability, 2012.

E. Luçon and W. Stannat, Mean field limit for disordered diffusions with singular interactions, 2013.

A. Manwani and C. Koch, Detecting and estimating signals in O, Faugeras et al./Large Deviations of a Stationary Neural Network with Learning 25

D. Mark, L. M. Mcdonnell, and . Ward, The benefits of noise in neural systems: bridging theory and experiment, Nature Reviews: Neuroscience, vol.12, 2011.

K. D. Miller and D. J. Mackay, The Role of Constraints in Hebbian Learning, Neural Computation, vol.1, issue.1, pp.100-126, 1996.
DOI : 10.1007/BF00198765

E. Oja, Simplified neuron model as a principal component analyzer, Journal of Mathematical Biology, vol.35, issue.3, pp.267-273, 1982.
DOI : 10.1007/BF00275687

S. Ostojic, N. Brunel, and V. Hakim, Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities, Journal of Computational Neuroscience, vol.97, issue.3, 2009.
DOI : 10.1007/s10827-008-0117-3

D. J. Pinto and G. B. Ermentrout, Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses, SIAM Journal on Applied Mathematics, vol.62, issue.1, pp.206-225, 2001.
DOI : 10.1137/S0036139900346453

G. Da, P. , and J. Zabczyk, Stochastic Equations in Infinite Dimensions, 1992.

E. Schneidman, M. J. Berry, R. Segev, and W. Bialek, Weak pairwise correlations imply strongly correlated network states in a neural population, Nature, vol.37, issue.7087, pp.4401007-1012, 2006.
DOI : 10.1038/nature04701

H. Sompolinsky, H. Yoon, K. Kang, and M. Shamir, Population coding in neuronal systems with correlated noise, Physical Review E, vol.64, issue.5, 2001.
DOI : 10.1103/PhysRevE.64.051904

A. Sznitman, Topics in propagation of chaos, Lecture Notes in Mathematics, vol.22, issue.1, pp.165-251, 1989.
DOI : 10.1070/SM1974v022n01ABEH001689

J. Touboul and B. Ermentrout, Finite-size and correlation-induced effects in mean-field dynamics, Journal of Computational Neuroscience, vol.13, issue.1???3, pp.453-484, 2011.
DOI : 10.1007/s10827-011-0320-5

URL : https://hal.archives-ouvertes.fr/hal-00846120

H. Tuckwell, Analytical and Simulation Results for the Stochastic Spatial Fitzhugh-Nagumo Model Neuron, Neural Computation, vol.5, issue.12, 2008.
DOI : 10.1214/aoms/1177692475

J. Duncan, S. H. Watts, and . Strogatz, Collective dynamics of smallworld networks, Nature, vol.393, 1998.