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arXiv · 2310.20517

Hyperuniformity of self-similar point processes

Daniel Roca
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Abstract

We study hyperuniformity of self-similar point processes arising from substitution rules in two dimensions. In particular, we derive a sufficient condition for hyperuniformity of these point processes only in terms of the associated substitution matrix. This condition applies to a wide class of examples for which hyperuniformity had not yet been established, including most well-known examples of planar self-similar tilings. In particular, we show that the Godr\`eche-Lan\c{c}on-Billard substitution rule gives rise to hyperuniform point processes with singular continuous diffraction. Furthermore, we prove that hyperuniformity is not an MLD invariant, contradicting standing conjectures.

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Daniel Roca. 2023-10-31. Hyperuniformity of self-similar point processes. https://arxiv.org/abs/2310.20517

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