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We consider a conductance based neural network inspired by the generalizedIntegrate and Fire model introduced by Rudolph and Destexhe. We show theexistence and uniqueness of a unique Gibbs distribution characterizing spiketrain statistics. The corresponding Gibbs potential is explicitly computed.These results hold in presence of a time-dependent stimulus and apply thereforeto non-stationary dynamics.

Statistics of spike trains in conductance-based neural networks: Rigorous results