论文标题
带有拉伸指数位移的随机分支步行的极端点过程
The extremal point process for branching random walk with stretched exponential displacements
论文作者
论文摘要
我们研究了分支随机步行，其中位移与分支机理无关，并具有拉伸指数分布。我们描述了颗粒在最右边粒子附近的位置在点过程收敛的角度。结果，我们为最右边粒子的位置提供了一个新的限制定理。我们的方法依赖于为I.I.D的总和提供精确的大偏差。随机变量在所谓的一个大跳跃制度之外具有拉伸指数分布。
We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle in terms of point process convergence. As a consequence we give a~new limit theorem for the position of the rightmost particle. Our methods rely on providing precise large deviations for sums of i.i.d. random variables with stretched exponential distributions outside the so-called one big jump regime.
