Collective behavior of independent scaled Brownian particles with renewal resetting

TL;DR

This paper investigates the collective fluctuations of independent scaled Brownian particles with renewal resetting, revealing universal fluctuation behavior and anomalous large deviation scaling in the system's center of mass.

Contribution

It introduces a detailed analysis of the collective behavior of scaled Brownian particles with resetting, highlighting universal fluctuation classes and large deviation anomalies.

Findings

Fluctuations of the system radius follow Gumbel universality.

Large deviations of the center of mass show anomalous scaling for H>1/2.

A singularity in the rate function indicates a 'big jump' effect.

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.