Collective behavior of independent scaled Brownian particles with renewal resetting
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914397292593152 |
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| author | Vilk, Ohad Meerson, Baruch |
| author_facet | Vilk, Ohad Meerson, Baruch |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Collective behavior of independent scaled Brownian particles with renewal resetting Vilk, Ohad Meerson, Baruch Statistical Mechanics 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. |
| title | Collective behavior of independent scaled Brownian particles with renewal resetting |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.21061 |