Negative large deviations of the front velocity of $N$-particle branching Brownian motion
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915056780836864 |
|---|---|
| author | Meerson, Baruch Sasorov, Pavel V. |
| author_facet | Meerson, Baruch Sasorov, Pavel V. |
| contents | We study negative large deviations of the long-time empirical front velocity of the center of mass of the one-sided $N$-BBM ($N$-particle branching Brownian motion) system in one dimension. Employing the macroscopic fluctuation theory, we study the probability that $c$ is smaller than the limiting front velocity $c_0$, predicted by the deterministic theory, or even becomes negative. To this end we determine the optimal path of the system, conditioned on the specified $c$. We show that for $c_0-c\ll c_0$ the properly defined rate function $s(c)$, coincides, up to a non-universal numerical factor, with the universal rate functions for front models belonging to the Fisher-Kolmogorov-Petrovsky-Piscounov universality class. For sufficiently large negative values of $c$, $s(c)$ approaches a simple bound, obtained under the assumption that the branching is completely suppressed during the whole time. Remarkably, for all $c\leq c_*$, where $c_*<0$ is a critical value that we find numerically, the rate function $s(c)$ is \emph{equal} to the simple bound. At the critical point $c=c_*$ the character of the optimal path changes, and the rate function exhibits a dynamical phase transition of second order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Negative large deviations of the front velocity of $N$-particle branching Brownian motion Meerson, Baruch Sasorov, Pavel V. Statistical Mechanics We study negative large deviations of the long-time empirical front velocity of the center of mass of the one-sided $N$-BBM ($N$-particle branching Brownian motion) system in one dimension. Employing the macroscopic fluctuation theory, we study the probability that $c$ is smaller than the limiting front velocity $c_0$, predicted by the deterministic theory, or even becomes negative. To this end we determine the optimal path of the system, conditioned on the specified $c$. We show that for $c_0-c\ll c_0$ the properly defined rate function $s(c)$, coincides, up to a non-universal numerical factor, with the universal rate functions for front models belonging to the Fisher-Kolmogorov-Petrovsky-Piscounov universality class. For sufficiently large negative values of $c$, $s(c)$ approaches a simple bound, obtained under the assumption that the branching is completely suppressed during the whole time. Remarkably, for all $c\leq c_*$, where $c_*<0$ is a critical value that we find numerically, the rate function $s(c)$ is \emph{equal} to the simple bound. At the critical point $c=c_*$ the character of the optimal path changes, and the rate function exhibits a dynamical phase transition of second order. |
| title | Negative large deviations of the front velocity of $N$-particle branching Brownian motion |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2408.14264 |