Pareto环境下分枝随机游动的标度极限与老化
Scaling limit and ageing for branching random walk in Pareto environment
摘要：
我们考虑格点上的分支随机游动，其中分支率由独立同分布给出。Pareto随机势我们表明，系统的粒子，以适当的方式重新缩放，收敛分布的缩放限制，这是有趣的，在其本身的权利。我们描述的极限对象作为一个不断增长的收集“百合花”建立在一个泊松点过程$\mathbb{R}^d$。作为主要定理的一个应用，我们证明了系统的极大化子具有老化性质。
英文摘要：
We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We show that the system of particles, rescaled in an appropriate way, converges in distribution to a scaling limit that is interesting in its own right. We describe the limit object as a growing collection of "lilypads" built on a Poisson point process in $\mathbb{R}^d$. As an application of our main theorem, we show that the maximizer of the system displays the ageing property.
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