Publications, preprints, notes, etc.

Fractals and dynamics

Sumset phenomena for fractals
In preparation.

Equidistribution from fractals
With Pablo Shmerkin.
In preparation.

Dynamics on fractal measures
preprint. arxiv.

Local entropy averages and projections of fractal measures.
With Pablo Shmerkin.
Annals of Mathematics, Volume 175 Number 3 (2012), 1001-1059, journal, arxiv.

Geometric rigidity of times-m invariant measures
To appear in the Journal of the European Mathematical Society, preprint, arxiv.

Probability measures on R^d are amenable
This unpublished note is the measure-theoretic analogue of the main lemma in my paper on ratio ergodic theorems.
It is apparently not known (let me know if you have seen it before). pdf

Ergodic theory

On the finite-dimensional marginals of shift-invariant measures
With J.-R. Chazottes , J.-M. Gambaudo , and E. Ugalde .
To appear in Ergodic Theory and Dynamical Systems, arxiv

Slow entropy and differentiable models for infinite measure preserving Z^d actions
Ergodic Theory and Dynamical Systems 32 (2012), 653--674 (special volume in memory of Dan Rudolph), journal, arxiv.

On zero-temperature limits of Gibbs states.
With J.R. Chazottes,
Communications in Mathematical Physics Volume 297, Number 1 / July, 2010, 265-281. journal, arxiv, Clarification.

A ratio ergodic theorem for multiparameter actions.
Journal of the European Mathematical Society 12 (2010), no. 2, 365--383. journal, arxiv.

Upcrossing inequalities for stationary sequences and applications to entropy and complexity
Ann. Probab. Volume 37, Number 6 (2009), 2135-2149. journal, arxiv.

On processes which cannot be distinguished by finitary observation.
With Yonatan Gutman,
Israel journal of Mathematics, Volume 164, Number 1 / March, 2008, journal, arxiv.

Return times, recurrence densities and entropy for actions of some discrete amenable groups,
Journal d'Analyse Mathematique, Volume 100, Number 1 / December, 2006, journal, arxiv.

Recurrence densities -- short version
This unbulished note is a short (6 pages, incl. intro & bib) version of the main result from the paper above, formulated for stationary processes (indexed by Z rather than a general amenable group).pdf

On one-sided and two sided ergodic averages of non-integrable functions.
This unpublished note answers a question raised by Yves Derriennic in the Fall 2008 semester on Ergodic Theory at MSRI. In retrospect it is a pretty simple thing. A similar proof was given independently by Benjamin Weiss. pdf.

Symbolic and topological dynamics (often with recursive-theoretic flavor)

On the finite-dimensional marginals of shift-invariant measures
With J.-R. Chazottes , J.-M. Gambaudo , and E. Ugalde .
To appear in Ergodic Theory and Dynamical Systems, arxiv

Isomorphism and embedding into Markov shifts off universally null sets
To appear in , Acta Applicandae Mathematicae, Hang Kim Memorial Volume. arxiv, preprint.

Inverses, products and cartesian powers of topologically deterministic maps
With Artur Siemaszko
Topological Methods in Nonlinear Analysis 39 (2012) No. 1, journal, arxiv.

Rohlin properties for $Z^d$-actions on the Cantor set.
Transactions of the AMS 364 (2012) No. 3, 1127--1143, journal, arxiv.

On notions of determinism in topological dynamics.
Ergodic Theory Dynamical Systems, 32 (2012) no. 1, 119--140, journal, arxiv.

Non-expansive directions for $Z^2$ actions.
Ergodic Theory Dynamical Systems 31 (2011), no. 1, 91--112, journal, arxiv.

A Characterization of the Entropies of Multidimensional Shifts of Finite Type.
With Tom Meyerovitch,
Annals of Mathematics Vol. 171 (2010), No. 3, 2011-2038, Journal, arxiv.

On the automorphism group of multidimensional SFTs.
Ergodic Theory Dynamical Systems (2010), 30, 809--840. journal, preprint.

On universality in multidimensional symbolic dynamics,
Discrete and Continuous Dynamical Systems S, Volume: 2, No. 2, 2009. arxiv, journal.

On the dynamics and recursive properties of multidimensional symbolic systems .
Inventiones Mathematica, Volume 176, Number 1, April, 2009. journal, preprint.

Genericity in Topological Dynamics.
Ergodic Theory Dynamical Systems (2008), 28 : 125-165, journal arxiv..

Probability

Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
With Michael Damron.
To appear in Annals of Applied Probability, Preprint, arxiv.

Upcrossing inequalities for stationary sequences and applications to entropy and complexity
Ann. Probab. Volume 37, Number 6 (2009), 2135-2149. journal, arxiv.

On processes which cannot be distinguished by finitary observation.
With Yonatan Gutman,
Israel journal of Mathematics, Volume 164, Number 1 / March, 2008, journal, arxiv.

Group theory

Averaging sequences and abelian rank in amenable groups.
Israel Journal of Mathematics, Volume 158, Number 1 / March, 2007, journal, arxiv..

Calculus Textbook

Together with my friends Yonatan Harel, Ittay Weiss and Ofek Shilon, I have written a calculus textbook to accompany the first year course given at the Hebrew University (the book is in Hebrew, of course). Here is the table of contents. The book is available from Academon Press. Corrections can be found on the book site.

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