The maximum of branching Brownian motion in $\mathbb{R}^d
We show that in branching Brownian motion (BBM) in $\mathbb{R}^d$, $d\geq 2$, the law of $R_t^*$, the maximum distance of a particle from the origin at time $t$, converges as $t\to\infty$ to the law of a randomly shifted Gumbel random variable.
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We show that in branching Brownian motion (BBM) in $\mathbb{R}^d$, $d\geq 2$,
the law of $R_t^*$, the maximum distance of a particle from the origin at time
$t$, converges as $t\to\infty$ to the law of a randomly shifted Gumbel random
variable. |
|---|---|
| DOI: | 10.48550/arxiv.2104.07698 |