4 papers
On a Constraint on Invariant Measures of Certain Cellular Automata
Matan Tal
In [7], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional…
The Return Times Theorem, Auto-Correlation and Sequences with an Empty Fourier-Bohr Spectrum
Matan Tal
This paper explores the proof by J. Bourgain, H. Furstenberg, Y. Katznelson and D.S. Ornstein of their return times theorem [2] and lights a corner in it regarding the role of auto…
Furstenberg's Times 2, Times 3 Conjecture (a Short Survey)
Matan Tal
The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theo…
Parsings of Stationary Processes, Stopping Times and the Fundamental Pointwise Convergence Theorems of Ergodic Theory
Matan Tal
The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is pr…