论文标题
分支布朗尼运动以较小的最大条件为条件
Branching Brownian motion conditioned on small maximum
论文作者
论文摘要
我们考虑在实际线路上的标准二元分支布朗尼运动。众所周知，所有活着的粒子的最大位置$ m_t $在时间$ t $中，$ m_t = \ sqrt {2} t - \ frac {3} {3} {2 \ sqrt {2}}}} \ log t $ t $在法律中收敛到随机移位的gumbel varible。 Derrida and Shi（2017）猜想了相应的较低偏差概率的精确渐近行为$ \ mathbb {p}（m_t \ leq \ leq \ sqrt {2}αt）$ for $α<1 $。我们验证了它们的猜想，并描述了布朗尼分支运动的定律，其条件为较小的最大值。
We consider a standard binary branching Brownian motion on the real line. It is known that the maximal position $M_t$ among all particles alive at time $t$, shifted by $m_t = \sqrt{2} t - \frac{3}{2\sqrt{2}} \log t$ converges in law to a randomly shifted Gumbel variable. Derrida and Shi (2017) conjectured the precise asymptotic behaviour of the corresponding lower deviation probability $\mathbb{P}(M_t \leq \sqrt{2}αt)$ for $α< 1$. We verify their conjecture, and describe the law of the branching Brownian motion conditioned on having a small maximum.
