Aperiodic order and spherical diffraction, I: auto-correlation of regular model sets
Artikel i vetenskaplig tidskrift, 2018

We study uniform and non-uniform model sets in arbitrary locally compact second countable (lcsc) groups, which provide a natural generalization of uniform model sets in locally compact abelian groups as defined by Meyer and used as mathematical models of quasi-crystals. We then define a notion of auto-correlation for subsets of finite local complexitiy in arbitrary lcsc groups, which generalizes Hof's classical definition beyond the class of amenable groups, and prov ide a formula for the auto-correlation of a regular model set. Along the way we show that the punctured hull of an arbitrary regular model set admits a unique invariant probability measure, even in the case where the punctured hull is non-compact and the group is non-amenable. In fact this measure is also the unique stationary measure with respect to any admissible probability measure.


37A45 (secondary)

52C23 (primary)



Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

T. Hartnick

Technion – Israel Institute of Technology

Felix Pogorzelski

Universität Leipzig

Proceedings of the London Mathematical Society

0024-6115 (ISSN) 1460-244X (eISSN)

Vol. 116 957-996


Algebra och logik

Sannolikhetsteori och statistik

Matematisk analys