ABSTRACT

In a catalytic branching random walk on a multidimensional lattice, with arbitrary finite total number of catalysts, in supercritical regime, when the vector coordinates of the random walk jump are assumed independent (or close to independent) to one another and have semi-exponential distributions, a limit theorem provides the almost sure normalized locations of the particles at the boundary between populated and empty areas. Contrary to the case of random walk increments with light distribution tails, the normalizing factor grows faster than linearly over time. The limit shape of the front in the case of semi-exponential tails is no longer convex, as it is in the case of light tails.

摘要

在具有任意有限催化剂总数的多维晶格上的催化分支随机游走中，在超临界状态下，当随机游走跳跃的矢量坐标被假定为彼此独立（或接近独立）并具有半指数分布时，极限定理提供了粒子在人口稠密区域和空旷区域之间的边界处几乎确定的归一化位置。与具有光分布尾部的随机游走增量的情况相反，归一化因子随着时间的推移增长快于线性增长。在半指数尾的情况下，前沿的极限形状不再是凸的，就像在轻尾的情况下一样。