Additive martingales of the branching Brownian motion
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913450939121664 |
|---|---|
| author | Chataignier, Louis |
| author_facet | Chataignier, Louis |
| contents | In this thesis, we study asymptotic properties of the standard branching Brownian motion, with a specific emphasis on the additive martingales at high temperature. We start by presenting classic and fundamental tools for our investigation. Subsequently, we establish various convergence results that enhance our understanding of the model. In particular, these results include the determination of particles contributing to the additive martingales, the description of the fluctuations of these martingales around their limits, and an approximation of the so-called overlap distribution. Regarding the latter, we believe this is the first time that such an approximation is given. Remarkably, we identify a specific regime in which stable distributions emerge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Additive martingales of the branching Brownian motion Chataignier, Louis Probability In this thesis, we study asymptotic properties of the standard branching Brownian motion, with a specific emphasis on the additive martingales at high temperature. We start by presenting classic and fundamental tools for our investigation. Subsequently, we establish various convergence results that enhance our understanding of the model. In particular, these results include the determination of particles contributing to the additive martingales, the description of the fluctuations of these martingales around their limits, and an approximation of the so-called overlap distribution. Regarding the latter, we believe this is the first time that such an approximation is given. Remarkably, we identify a specific regime in which stable distributions emerge. |
| title | Additive martingales of the branching Brownian motion |
| topic | Probability |
| url | https://arxiv.org/abs/2407.20227 |