Dandekar, Rahul; P. L. Krapivsky and Krone Mallick
We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the |x - y|-s Riesz potential, causing the overdamped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for 0 < s < 1, the standard deviations s of both quantities grow as t 2(1+s) . When s > 1, the interactions are effectively short-ranged, and the universal 1 subdiffusive t 4 growth emerges with only amplitude depending on the exponent s. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.