Notions of disorder for random substitutions

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• Philipp Gohlke (Universität Bielefeld)
• Thursday 09 December 2021, 15:00-16:00
• Zoom.

If you have a question about this talk, please contact David Craven.

Substitutions are a classic tool to produce self-similar structures with a long-range order. The corresponding shift-dynamical systems can be deemed to be relatively ordered as they have vanishing entropy, and are often isomorphic to a rotation on a locally compact abelian group. By locally randomizing the substitution rule, we obtain dynamical systems that are much more disordered in a measure-theoretic, topological and combinatorial sense. At the same time, under appropriate conditions, they maintain long-range correlations, presenting themselves in a non-trivial pure point part of the diffraction measure. In this talk, we will discuss how to assess several notions of disorder in the context of random substitutions, including quantitative bounds for topological and measure-theoretic entropy.

This talk is based on joint work with A. Mitchell, D. Rust, T. Samuel, and T. Spindeler.

This talk is part of the Topology and Dynamics seminar series.

This talk is included in these lists:

• School of Mathematics events
• Topology and Dynamics seminar
• Zoom

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