几何结晶过程的遍历性
Ergodic properties of geometrical crystallization processes, I
摘要：
在这里，我们感兴趣的是一个出生和生长过程中，细菌出生根据泊松点过程与不变下平移空间强度措施。细菌可以在自由空间中出生，然后开始生长，直到占据可用空间。为了考虑不同的生长方式，我们通过晶体的几何性质描述了每一时刻的晶体。在这个一般框架中，结晶过程可以通过随机场来表征，该随机场在晶体第一次到达空间状态中的点时给出该点。在一般条件下证明了该随机场在遍历论意义下是混合的，并得到了绝对正则性系数的估计。
英文摘要：
We are interested here in a birth-and-growth process where germs are born according to a Poisson point process with invariant under translation in space intensity measure. The germs can be born in free space and then start growing until occupying the available space. In order to consider various way of growing, we describe the crystals at each time through their geometrical properties. In this general framework, the crystallization process can be caracterized by the random field giving for a point in the space state the first time this point is reached by a crystal. We prove under general conditions that this random field is mixing in the sens of ergodic theory and obtain estimates for the coefficient of absolute regularity.
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