Self Affine Delone Sets and Deviation Phenomena

Scott Edward Schmieding, Rodrigo Treviño*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the growth of norms of ergodic integrals for the translation action on spaces coming from expansive, self-affine Delone sets. The linear map giving the self-affinity induces a renormalization map on the pattern space and we show that the rate of growth of ergodic integrals is controlled by the induced action of the renormalizing map on the cohomology of the pattern space up to boundary errors. We explore the consequences for the diffraction of such Delone sets, and explore in detail what the picture is for substitution tilings as well as for cut and project sets which are self-affine. We also explicitly compute some examples.

Original languageEnglish (US)
Pages (from-to)1071-1112
Number of pages42
JournalCommunications in Mathematical Physics
Volume357
Issue number3
DOIs
StatePublished - Feb 1 2018

Fingerprint

Self-affine
Deviation
deviation
Self-affinity
homology
Linear map
Tiling
norms
Renormalization
affinity
Substitution
Diffraction
Cohomology
substitutes
Norm
diffraction

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Schmieding, Scott Edward ; Treviño, Rodrigo. / Self Affine Delone Sets and Deviation Phenomena. In: Communications in Mathematical Physics. 2018 ; Vol. 357, No. 3. pp. 1071-1112.
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Self Affine Delone Sets and Deviation Phenomena. / Schmieding, Scott Edward; Treviño, Rodrigo.

In: Communications in Mathematical Physics, Vol. 357, No. 3, 01.02.2018, p. 1071-1112.

Research output: Contribution to journalArticle

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