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Pair correlation of dilute Active Brownian Particles: from low activity dipolar correction to high activity algebraic depletion wings

We study the pair correlation of Active Brownian Particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: while particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.