Scholarlink

<p>For <i>N</i> compatible substitution rules on <i>M</i> prototiles <i>t</i><sub>1</sub>, …, <i>t</i><sub><i>M</i></sub>, consider tilings and tiling spaces constructed by applying the different substitution rules at random. These give (globally) random substitution tilings. In this paper I obtain bounds for the growth on twisted ergodic integrals for the ℝ<sup><i>d</i></sup> action on the tiling space which give lower bounds on the lower local dimension of spectral measures. For functions with some extra regularity, uniform bounds on the lower local dimension are obtained. The results here extend results of Bufetov–Solomyak [BS21] to tilings of higher dimensions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantitative weak mixing for random substitution tilings

  • 期刊论文

  • 发表日期：

    2025年5月9日

查看全文
  • Rodrigo Treviño

摘要

For N compatible substitution rules on M prototiles t1, …, tM, consider tilings and tiling spaces constructed by applying the different substitution rules at random. These give (globally) random substitution tilings. In this paper I obtain bounds for the growth on twisted ergodic integrals for the ℝd action on the tiling space which give lower bounds on the lower local dimension of spectral measures. For functions with some extra regularity, uniform bounds on the lower local dimension are obtained. The results here extend results of Bufetov–Solomyak [BS21] to tilings of higher dimensions.