论文标题
分支布朗运动的拉伸尖端中粒子数密度的概率图片
Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion
论文作者
论文摘要
在一维分支布朗尼运动的随机图片的框架中，我们计算了最右边$ t $的粒子数量的概率密度，我们会很大，当时这个极端粒子的条件是在预定的位置到达预期位置$ x_t $ x_t $ toss $ x_t $ x_t $ toss $ x_t $ x_t $ the Thecture to Thecture to Thecred Tocient to Tresent Toperion $ M_T $。我们恢复了以前的注射事实，即粒子的典型数量密度是距离铅粒子的左侧$δ$的典型数量密度，而当$Δ$和$δ$和$ x_t-Δ-δ-m_T $都大，小于平均数量密度，而平均数量密度是成比例的因素，而与$ e^{ - ζδ^{2/3}} $的$ e^{ - ζΔ我们的图片导致了粒子数的概率密度的表达，可以从中推断出$ζ$的值。
In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme particle is conditioned to arrive at a predefined position $x_T$ chosen far ahead of its expected position $m_T$. We recover the previously-conjectured fact that the typical number density of particles a distance $Δ$ to the left of the lead particle, when both $Δ$ and $x_T-Δ-m_T$ are large, is smaller than the mean number density by a factor proportional to $e^{-ζΔ^{2/3}}$, where $ζ$ is a constant that was so far undetermined. Our picture leads to an expression for the probability density of the particle number, from which a value for $ζ$ may be inferred.
