随机燃烧模型中锋面的波动
Fluctuations of the front in a stochastic combustion model
摘要：
考虑一维格点$\bf Z$上的相互作用粒子系统模拟燃烧。该过程取决于两个整数参数$2\le a<M<\infty$。粒子作为连续时间简单对称随机游动独立运动，除了1。当一个粒子跳到一个之前没有被任何粒子访问过的位置时，它分支成$a$粒子; 2.当一个粒子跳跃到含有$M$粒子的位置时，它被湮灭。我们从一个配置开始，所有网站的左边的原点已经访问过，并研究了大数定律和中心极限定理的$r_t$，最右边的网站在时间$t$。的证据是基于建设的更新结构，导致再生时间的定义，可以进行良好的尾部估计。
英文摘要：
We consider an interacting particle system on the one dimensional lattice $\bf Z$ modeling combustion. The process depends on two integer parameters $2\le a<M<\infty$. Particles move independently as continuous time simple symmetric random walks except that 1. When a particle jumps to a site which has not been previously visited by any particle, it branches into $a$ particles; 2. When a particle jumps to a site with $M$ particles, it is annihilated. We start from a configuration where all sites to the left of the origin have been previously visited and study the law of large numbers and central limit theorem for $r_t$, the rightmost visited site at time $t$. The proofs are based on the construction of a renewal structure leading to a definition of regeneration times for which good tail estimates can be performed.
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