不同线性尺度上的齐次化、有界鞅和双尺度Shuffle极限
Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit
摘要：
在本文中，我们考虑两个尺度的极限得到的均匀化期间，每一个时期是前一个的整数倍。我们建立，直到措施保持重排，这些两个规模的限制形成一个鞅是有界的：重新安排的两个规模的限制本身都强收敛于$\mathrm{L}^2$和几乎处处不在时，周期趋于$+\infty$。此限制称为双尺度随机化限制，包含序列中所有双尺度限制中存在的所有信息。
英文摘要：
In this paper, we consider two-scale limits obtained with increasing homogenization periods, each period being an entire multiple of the previous one. We establish that, up to a measure preserving rearrangement, these two-scale limits form a martingale which is bounded: the rearranged two-scale limits themselves converge both strongly in $\mathrm{L}^2$ and almost everywhere when the period tends to $+\infty$. This limit, called the Two-Scale Shuffle limit, contains all the information present in all the two-scale limits in the sequence.
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