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Strong positional correlations between particles render the diffusion of atracer particle in a single file anomalous and non-Markovian. While ensembleaverage observables of tracer particles are nowadays well understood, little isknown about the statistics of the corresponding functionals, i.e. thetime-average observables. It even remains unclear how the non-Markovian natureemerges from correlations between particle trajectories at different times.Here, we first present rigorous results for fluctuations and two-tagcorrelations of general bounded functionals of ergodic Markov processes with adiagonalizable propagator. They relate the statistics of functionals onarbitrary time-scales to the relaxation eigenspectrum. Then we study taggedparticle local times -- the time a tracer particle spends at some predefinedlocation along a single trajectory up to a time t. Exact results are derivedfor one- and two-tag local times, which reveal how the individual particles'histories become correlated at higher densities because each consecutivedisplacement along a trajectory requires collective rearrangements. Our resultsunveil the intricate meaning of projection-induced memory on a trajectorylevel, invisible to ensemble-average observables, and allow for a detailedanalysis of single-file experiments probing tagged particle explorationstatistics.

Unfolding Tagged Particle Histories in Single-File Diffusion: Exact Single- and Two-Tag Local Times Beyond Large Deviation Theory