Scaling limits of solitons in the box-ball system
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910928678682624 |
|---|---|
| author | Olla, Stefano Sasada, Makiko Suda, Hayate |
| author_facet | Olla, Stefano Sasada, Makiko Suda, Hayate |
| contents | We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the large deviation principle for the tagged soliton under certain shift-ergodic invariant distributions, including Bernoulli product measures and two-sided Markov distributions. Furthermore, in the diffusive space-time scaling, we show that two tagged solitons converge to the same Brownian motion even if they are macroscopically far apart. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14818 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling limits of solitons in the box-ball system Olla, Stefano Sasada, Makiko Suda, Hayate Probability 37B15(primary), 82C22, 82C23 (secondary) We study the space-time scaling limits of solitons in the box-ball system with random initial distribution. In particular, we show that any recentered tagged soliton converges to a Brownian motion in the diffusive space-time scale, and also prove the large deviation principle for the tagged soliton under certain shift-ergodic invariant distributions, including Bernoulli product measures and two-sided Markov distributions. Furthermore, in the diffusive space-time scaling, we show that two tagged solitons converge to the same Brownian motion even if they are macroscopically far apart. |
| title | Scaling limits of solitons in the box-ball system |
| topic | Probability 37B15(primary), 82C22, 82C23 (secondary) |
| url | https://arxiv.org/abs/2411.14818 |