  Distributions of neuronal activity within cortical circuits are often found
to display highly skewed shapes with many neurons emitting action potentials at
low or vanishing rates, while some are active at high rates. Theoretical
studies were able to reproduce such distributions, but come with a lack of
mathematical tractability, preventing a deeper understanding of the impact of
model parameters. In this study, using the Gauss-Rice neuron model, we present
a balanced-state cortical circuit model for which the firing rate distribution
can be exactly calculated. It offers selfconsistent solutions to recurrent
neuronal networks and allows for the combination of multiple neuronal
populations, with single or multiple synaptic receptors (e.g. AMPA and NMDA in
excitatory populations), paving the way for a deeper understanding of how
firing rate distributions are impacted by single neuron or synaptic properties.
