一维X+Y-->2X模型中锋面的起伏
Fluctuations of the front in a one dimensional model of X+Y-->2X
摘要：
考虑整数格点上反应$X+Y\to 2X$的模型，其中$Y$粒子不运动，而$X$粒子作为独立的连续时间简单对称随机游动运动. $Y$颗粒在接触时瞬间转化为$X$颗粒。我们从原点右侧的每个站点的$Y$粒子的固定数量$a\ge 1$开始，并定义原点左侧的$X$粒子的一类配置，其具有具有指定指数权重的有限$l^1$范数。从任何配置的$X$粒子的左边的原点在这样一个类，我们证明了一个中心极限定理的位置最右访问网站的$X$粒子。
英文摘要：
We consider a model of the reaction $X+Y\to 2X$ on the integer lattice in which $Y$ particles do not move while $X$ particles move as independent continuous time, simple symmetric random walks. $Y$ particles are transformed instantaneously to $X$ particles upon contact. We start with a fixed number $a\ge 1$ of $Y$ particles at each site to the right of the origin, and define a class of configurations of the $X$ particles to the left of the origin having a finite $l^1$ norm with a specified exponential weight. Starting from any configuration of $X$ particles to the left of the origin within such a class, we prove a central limit theorem for the position of the rightmost visited site of the $X$ particles.
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