论文标题
与选择的间隔碎片：等分分配和标记片段的演变
Interval fragmentations with choice: equidistribution and the evolution of tagged fragments
论文作者
论文摘要
我们在点过程中考虑了马尔可夫的演变，即$ψ$ - 在单位间隔上，根据一个仅取决于现有点配置的间距的规则，添加了点。选择了间距后，在其中均匀地添加了一个新点。在作者和Junge的先前工作的基础上，我们表明，在这种过程中，积分的经验分布总是在对规则的轻度假设下等级，从而概括了Junge的工作。 本文的主要部分致力于研究特定的生长过程 - 覆盖过程或细胞过程，这是一种分段 - 确定的马尔可夫过程（PDMP）。此过程代表了$ψ$ - 过程的大小偏见采样的线性化版本。我们表明，该PDMP是ergodic的，并开发了它的半群理论，以表明它描述了$ψ$ - 过程的线性化版本。该PDMP已出现在其他情况下，从某种意义上说，我们在最低限度的假设下发展了其理论。
We consider a Markovian evolution on point processes, the $Ψ$--process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a new point is added uniformly within it. Building on previous work of the authors and of Junge, we show that the empirical distribution of points in such a process is always equidistributed under mild assumptions on the rule, generalizing work of Junge. A major portion of this article is devoted to the study of a particular growth--fragmentation process, or cell process, which is a type of piecewise--deterministic Markov process (PDMP). This process represents a linearized version of a size--biased sampling from the $Ψ$--process. We show that this PDMP is ergodic and develop the semigroup theory of it, to show that it describes a linearized version of the $Ψ$--process. This PDMP has appeared in other contexts, and in some sense we develop its theory under minimal assumptions.
