Collective behavior of independent scaled Brownian particles with renewal resetting

Abstract

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, $D(t)\sim t^{2H-1}$, 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 \emph{single} particle undergoing the sBm with renewal resetting [Bodrova et al., Phys. Rev. E \textbf{100}, 012120 (2019)], we study the statistics of the system radius $\ell$ and of the center of mass (COM) of $N\gg 1$ particles. Typical fluctuations of $\ell$ fall under the Gumbel universality class for all $H>0$, and we use extreme value statistics to calculate the moments of $\ell$. 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 $N\to \infty$, which is caused by a ``big jump" effect.

20 single-column pages, 5 figures