Stationary map coloring (2009)
Angel, Omer, Benjamini, Itai, Gurel-Gurevich, Ori, Meyerovitch, Tom, Peled, Ron
We consider a planar Poisson process and its associated Voronoi map. We show that there is a proper coloring with 6 colors of the map which is a deterministic isometry-equivariant function of the...
Gibbs and equilibrium measures for some families of subshifts (2009)
For SFTs, any equilibrium measure is Gibbs, as long a $f$ has $d$-summable variation. This is a theorem of Lanford and Ruelle. Conversely, a theorem of Dobru{\v{s}}in states that for...
We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth rates of the number of admissible finite configurations. Extending an...
Quasi-factors for infinite-measure preserving transformations (2008)
This paper is a study of Glasner's definition of quasi-factors in the setting of infinite-measure preserving system. The existence of a system with zero Krengel entropy and a quasi-factor with...
Poisson suspensions and entropy for infinite transformations (2008)
Janvresse, Elise, Meyerovitch, Tom, Roy, Emmanuel, De La Rue, Thierry
The Poisson entropy of an infinite-measure-preserving transformation is defined as the Kolmogorov entropy of its Poisson suspension. In this article, we relate Poisson entropy with other definitions...
We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.
A Characterization of the Entropies of Multidimensional Shifts of Finite Type (2007)
Hochman, Michael, Meyerovitch, Tom
We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number $h\geq 0$ is the entropy of such an...
Finite entropy for multidimensional cellular automata (2007)
Let $X=S^G$ where $G$ is a countable group and $S$ is a finite set. A cellular automaton (CA) is an endomorphism $T : X \to X$ (continuous, commuting with the action of $G$). Shereshevsky (1993)...
Absolutely continuous, invariant measures for dissipative, ergodic transformations (2005)
Aaronson, Jon., Meyerovitch, Tom
We show that a dissipative, ergodic measure preserving transformation of a sigma-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is...
Double-Tail Invariant Measures of the Dyck Shift (2004)
In a previous paper by the author, it was shown that the One sided Dyck is uniquely ergodic with respect to the one sided-tail relation, where the tail invariant probability is also shift invariant...
Tail Invariant Measures of the Dyck Shift (2004)
We show that the one-sided Dyck shift has a unique tail invariant topologically $\sigma$-finite measure (up to scaling). This invariant measure of the one sided Dyck turns out to be a shift-invariant...
The research work for this thesis has been carried out at Tel-Aviv University under the supervision of Prof. Jon Aaronson