We experimentally study a system of $N=4$ two-dimensional Brownian particles, each confined in a harmonic trap with identical stiffness. The stiffness switches simultaneously between two values at random Poissonian times. This collective switching drives the system into a nonequilibrium stationary state with strong long-range correlations between the positions of the particles. Remarkably, we find that, despite the presence of hydrodynamic interactions between the particles mediated by the surrounding fluid, the statistics of some observables are insensitive to hydrodynamic interactions and are well described by the noninteracting theory. Comparing with exact theoretical predictions for noninteracting particles, we observe excellent agreement between theory and experiments for three such observables, namely, the correlations between particles, extreme value, and order statistics (maxima, minima, and ranked positions) and the full counting statistics (i.e., the distribution of the number of particles in a finite interval $[-L,L]$ around the trap center).

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• Brownian motion
• Fluctuations & noise
• Stochastic resetting
• Full counting statistics