同质多型碎裂
Homogenenous Multitype Fragmentations
摘要：
在\cite{RFC}中定义的均匀质量碎裂，描述的是随着时间的推移，一个物体的碎片质量集合的演变。在这里，我们表明，这个模型可以通过考虑的类型的碎片，其中一个类型可以表示，例如，一个几何形状，并可以采取许多值也可以丰富。在这种情况下，随机标记的碎片的动力学在碎片分析中起着至关重要的作用。它们由马尔可夫加性过程确定，其分布明确取决于碎片的特征。作为应用，我们给出了它与多型分枝随机游动的联系，得到了路径型中心极限定理的多型类似定理和碎片经验分布的大偏差估计.
英文摘要：
A homogeneous mass-fragmentation, as it has been defined in \cite{RFC}, describes the evolution of the collection of masses of fragments of an object which breaks down into pieces as time passes. Here, we show that this model can be enriched by considering also the types of the fragments, where a type may represent, for instance, a geometrical shape, and can take finitely many values. In this setting, the dynamics of a randomly tagged fragment play a crucial role in the analysis of the fragmentation. They are determined by a Markov additive process whose distribution depends explicitly on the characteristics of the fragmentation. As applications, we make explicit the connexion with multitype branching random walks, and obtain multitype analogs of the pathwise central limit theorem and large deviation estimates for the empirical distribution of fragments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
