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Given a population of interconnected input-output agents repeatedly exposedto independent random inputs, we talk of correlated variability when agents'outputs are variable (i.e., they change randomly at each input repetition) butcorrelated (i.e., they do not vary independently across input repetitions).Correlated variability appears at multiple levels in neuronal systems, from themolecular level of protein expression to the electrical level of neuronalexcitability, but its functions and origins are still debated. Motivated byadvancing our understanding of correlated variability, we introduce the(linear) "correlated variability control problem" as the problem of controllingsteady-state correlations in a linear dynamical network in which agents receiveindependent random inputs. Although simple, the chosen setting revealsimportant connections between network structure, in particular, the existenceand the dimension of dominant (i.e., slow) dynamics in the network, and theemergence of correlated variability.

The correlated variability control problem: a dominant approach