Publications, preprints, notes, etc.

Preprints / in review

Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
With Michael Damron.
preprint, arxiv.

Dynamics on fractal measures
preprint. arxiv.

Published / accepted

Local entropy averages and projections of fractal measures.
With Pablo Shmerkin.
To appear in Annals of Mathematics, arxiv, preprint

Slow entropy and differentiable models for infinite measure preserving Z^d actions
To appear in Ergodic Theory and Dynamical Systems (special volume in memory of Dan Rudolph), preprint, arxiv

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

Inverses, products and cartesian powers of topologically deterministic maps
With Artur Siemaszko
To appear in Topological Methods in Nonlinear Analysis, preprint, arxiv

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

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

Rohlin properties for $Z^d$-actions on the Cantor set.
To appear in Transactions of the AMS, preprint, arxiv

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

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

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

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

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

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

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. preprint, journal

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

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

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

Notes

Notes on information theory (source coding).
These are rough notes from a short course I gave for advanced undergraduates on information theory, focusing on source coding. I would recommend some background in elementary probability, athough the notes include a brief review. Topics include: Kraft's ineuqality and Shannon's coding theorems, definition and properties of entropy, mean entropy for stationary processes, Markov chains and LLN for them, Shannon-McMillan theorem for Markov chains, and the Lempel-Ziv universal coding algorithm. pdf.

On one-sided and two sided ergodic averages of non-integrable functions.
This 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.

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

Recurrence densities for ergodic processes
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

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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