Distribution of particles near the front in supercritical branching Brownian motion with compactly supported branching
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912827443249152 |
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| author | Hebbar, Pratima Koralov, Leonid |
| author_facet | Hebbar, Pratima Koralov, Leonid |
| contents | We investigate the long-time behavior of a $d-$dimensional supercritical branching Brownian motion with a compactly supported branching potential. It is known that, for $\mathbf{v}\in \mathbb{R}^d$, all the moments of the normalized number of particles in a bounded domain centered at $\mathbf{v} t$ converge, as $t \rightarrow \infty$, provided that $\|\mathbf{v}\|$ is strictly less than the asymptotic speed of the front. The limiting distribution does not depend on $\mathbf{v}$. Using sharp asymptotics for the solutions of parabolic PDEs with compact potential, we prove that the normalized number of particles in a bounded time-dependent domain located near the front converges in distribution and with all the moments. The limit, however, now depends on the asymptotic location of the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distribution of particles near the front in supercritical branching Brownian motion with compactly supported branching Hebbar, Pratima Koralov, Leonid Probability 60J80, 60J60, 35K10 We investigate the long-time behavior of a $d-$dimensional supercritical branching Brownian motion with a compactly supported branching potential. It is known that, for $\mathbf{v}\in \mathbb{R}^d$, all the moments of the normalized number of particles in a bounded domain centered at $\mathbf{v} t$ converge, as $t \rightarrow \infty$, provided that $\|\mathbf{v}\|$ is strictly less than the asymptotic speed of the front. The limiting distribution does not depend on $\mathbf{v}$. Using sharp asymptotics for the solutions of parabolic PDEs with compact potential, we prove that the normalized number of particles in a bounded time-dependent domain located near the front converges in distribution and with all the moments. The limit, however, now depends on the asymptotic location of the domain. |
| title | Distribution of particles near the front in supercritical branching Brownian motion with compactly supported branching |
| topic | Probability 60J80, 60J60, 35K10 |
| url | https://arxiv.org/abs/2601.10833 |