Collective behavior of independent scaled Brownian particles with renewal resetting

We study fluctuations of an ensemble of N independent particles undergoing anomalous diffusion with random renewal resetting. The anomalous diffusion is modeled by the scaled Brownian motion (sBm): a Gaussian process, characterized by a power-law time dependence of the diffusion coefficient, D(t)∼t^2H−1, where H>0. The particles independently reset to the origin, and each particle's clock is set to zero upon spatial resetting. Employing the known steady-state position distribution of a single particle undergoing the sBm with renewal resetting (Bodrova et al., 2019), we study the statistics of the system radius ℓ and of the center of mass (COM) of N≫1 particles. Typical fluctuations of ℓ fall under the Gumbel universality class for all H>0, and we use extreme value statistics to calculate the moments of ℓ. We show that, for H>1/2, large deviations of the COM exhibit an anomalous scaling behavior. We also uncover a singularity in the corresponding rate function at N→∞, which is caused by a “big jump” effect.