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arXiv · 1209.6145

Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit

Kévin Santugini-Repiquet
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Abstract

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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Kévin Santugini-Repiquet. 2012-09-27. Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit. https://doi.org/10.1051/cocv%2F2012039.

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