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We consider a system of non-interacting Brownian particles on a line with astep-like initial condition, and we investigate the behavior of the local timeat the origin at large times. We compute the mean and the variance of the localtime, and we show that the memory effects are governed by the Fano factorassociated with the initial condition. For the uniform initial condition, weshow that the probability distribution of the local time admits a largedeviation form, and we compute the corresponding large deviation functions forthe annealed and quenched averaging schemes. The two resulting large deviationfunctions are very different. Our analytical results are supported by extensivenumerical simulations.

Local time of a system of Brownian particles on the line with steplike initial condition