7 citations · 19 across the 9 of their papers we have counts for
11 papers
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…
A dichotomy for bounded displacement equivalence of Delone sets
Yotam Smilansky, Yaar Solomon
We prove that in every compact space of Delone sets in which is minimal with respect to the action by translations, either all Delone sets are uniformly spread, or c…
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…
Bounded Displacement Non-Equivalence In Substitution Tilings
Dirk Frettlöh, Yotam Smilansky, Yaar Solomon
In the study of aperiodic order and mathematical models of quasicrystals, questions regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the bo…
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…
The Distribution of Path Lengths On Directed Weighted Graphs
Avner Kiro, Yotam Smilansky, Uzy Smilansky
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate…
On the Function Field Analogue of Landau's Theorem on Sums of Squares
Lior Bary-Soroker, Yotam Smilansky, Adva Wolf
This paper deals with function field analogues of the famous theorem of Landau which gives the asymptotic density of sums of two squares in . We define the analogue of…
Sum of Two Squares - Pair Correlation and Distribution in Short Intervals
Yotam Smilansky
In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and refo…