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Persistent activity observed in neurophysiological experiments in monkeys is thought to be the neuronal correlate of working memory. Over the last decade, network modellers have strived to reproduce the main features of these experiments. In particular, attractor network models have been proposed in which there is a coexistence between a non-selective attractor state with low background activity with selective attractor states in which sub-groups of neurons fire at rates which are higher (but not much higher) than background rates. A recent detailed statistical analysis of the data seems however to challenge such attractor models: the data indicates that firing during persistent activity is highly irregular (with an average CV larger than 1), while models predict a more regular firing process (CV smaller than 1). We discuss here recent proposals that allow to reproduce this feature of the experiments.