论文标题
周期介质中分支扩散过程的渐近行为
Asymptotic behavior of branching diffusion processes in periodic media
论文作者
论文摘要
我们研究周期培养基中分支扩散过程的渐近行为。对于超临界分支过程，我们根据域中的距离距离界面的距离与大部分粒子所在的区域的距离区分了归一数量的粒子数量的两种类型的行为。在及时线性地生长的距离上，我们观察到间歇性（即，$ k $ - 第3刻的时间占主导地位的$ k $ - 第一个时刻的$ k $ - 对于一些$ k $而言），而在及时生长的距离上，我们显示了所有时刻的融合。我们分析中的一个关键成分是对分支过程的过渡内核的尖锐估计，有效期可在距离初始粒子位置的时间距离内直至线性。
We study the asymptotic behavior of branching diffusion processes in periodic media. For a super-critical branching process, we distinguish two types of behavior for the normalized number of particles in a bounded domain, depending on the distance of the domain from the region where the bulk of the particles is located. At distances that grow linearly in time, we observe intermittency (i.e., the $k$-th moment dominates the $k$-th power of the first moment for some $k$), while, at distances that grow sub-linearly in time, we show that all the moments converge. A key ingredient in our analysis is a sharp estimate of the transition kernel for the branching process, valid up to linear in time distances from the location of the initial particle.
