论文标题
具有有限细胞大小的生长碎片化过程的大量法律的强大定律
Strong laws of large numbers for a growth-fragmentation process with bounded cell sizes
论文作者
论文摘要
生长碎片处理过程模型的细胞系统，这些系统随着时间的流逝而连续生长，然后碎片成较小的碎片。通常，平均而言，系统中的细胞数量表现出异步指数生长，并且在补偿这一点后，细胞尺寸的分布会收敛到渐近谱。但是，系统的长期随机行为更加精致，迄今为止，它几乎肯定没有探索。在本文中，我们研究了一个细胞大小在上面有限的生长碎片碎片化过程，并证明存在具有不同长期行为的政权。
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon compensating for this, the distribution of cell sizes converges to an asymptotic profile. However, the long-term stochastic behaviour of the system is more delicate, and its almost sure asymptotics have been so far largely unexplored. In this article, we study a growth-fragmentation process whose cell sizes are bounded above, and prove the existence of regimes with differing almost sure long-term behaviour.
