In this paper, we investigate the size of a bidimensional fragmentation process. A rectangle of dimensions x and y is considered; it is split into four subrectangles with some probability that depends on x and y; we iterate until the stop of the process. The total number of the all the obtained rectangles at the end of the process satisfies some equality in distribution which is resolved by the contraction method and by some tools on integral equations.

中文翻译：

---

非齐次二元分裂过程：通过收缩法的渐近分布

在本文中，我们研究了二维碎片化过程的大小。考虑尺寸为x和y 的矩形；它被分成四个子矩形，概率取决于x和y；我们迭代直到过程停止。过程结束时得到的所有矩形的总数满足一定的分布等式，这是通过收缩方法和积分方程的一些工具解决的。