7 citations · 19 across the 9 of their papers we have counts for
6 papers · 1 filter
An exceptional set of uniformly spread Kakutani tilings of the line
Yotam Smilansky
The α-Kakutani substitution rule splits the unit interval into two subintervals of lengths alpha and 1 - α, for a fixed α in (0,1). A simple inflation-substitution procedure produc…
Discrepancy and rectifiability of almost linearly repetitive Delone sets
Yotam Smilansky, Yaar Solomon
We extend a discrepancy bound of Lagarias and Pleasants for local weight distributions on linearly repetitive Delone sets and show that a similar bound holds also for the more gene…
Statistics and gap distributions in random Kakutani partitions and multiscale substitution tilings
Yotam Smilansky
We study statistics of tiles in random incommensurable Kakutani sequences of partitions in . We provide explicit formulas that illustrate the dependence on the combin…
Classification and statistics of cut and project sets
René Rühr, Yotam Smilansky, Barak Weiss
We define Ratner-Marklof-Strombergsson measures. These are probability measures supported on cut-and-project sets in R^d (d > 1) which are invariant and ergodic for the action of t…
Multiscale Substitution Tilings
Yotam Smilansky, Yaar Solomon
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes…
Uniform Distribution of Kakutani Partitions Generated By Substitution Schemes
Yotam Smilansky
Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile…