publications
Article
Delone sets with finite local ,complexity: linear repetitivity versus positivity of weights |
Besbes Adnene, Daniel Lenz, Michel Boshernitzan, 2012 |
Discrete and Computational Geometry , 49, 2, 335-347 , Décembre 2012 |
Résumé
We consider Delone sets with finite local complexity. We characterize the
validity of a subadditive ergodic theorem by uniform positivity of certain weights.
The latter can be considered to be an averaged version of linear repetitivity. In this
context, we show that linear repetitivity is equivalent to positivity of weights combined
with a certain balancedness of the shape of return patterns.
We consider Delone sets with finite local complexity. We characterize thevalidity of a subadditive ergodic theorem by uniform positivity of certain weights.The latter can be considered to be an averaged version of linear repetitivity. In thiscontext, we show that linear repetitivity is equivalent to positivity of weights combinedwith a certain balancedness of the shape of return patterns.
