Publications, preprints, notes, etc.

Here is the list of publications sorted by topic.

Preprints / in review

Hausdorff dimension of planar self-affine sets and measures with overlaps
With Ariel Rapaport.
preprint, arxiv

Dynamics on fractal measures
preprint. arxiv.

Published / accepted

Hausdorff dimension of planar self-affine sets and measures
With Balázs Bárány and Ariel Rapaport.
To appear in Inventiones Mathematicae, preprint, arxiv

On self-similar sets with overlaps and inverse theorems for entropy in R^d
To appear in Memoires of the AMS, preprint, arxiv.

Every Borel automorphism without finite invariant measures admits a two-set generator
Journal of the European Mathematical Society, Volume 21, Issue 1, 2019, pp. 271–317, journal, arxiv.

Smooth symmetries of xa invariant sets
Journal of Modern Dynamics, 2018, vol 13, pp 187-197. journal, arxiv.

Self embeddings of Bedford-McMullen carpets
With Amir Algom.
To appear in Ergodic Theory Dynamical Systems, journal, arxiv.

On the dimension of Furstenberg measure for SL(2,R) random matrix products
With Boris Solomyak.
Inventiones Mathematicae 2017, Volume 210, Issue 3, pp 815–875, journal, arxiv , Clarification.

On the Turing Degree Spectra of Minimal Subshifts
With Pascal Vanier.
CSR 2017, pp 154-161, journal, arxiv.

Some problems on the boundary of fractal geometry and additive combinatorics
Recent Developments in Fractals and Related Fields, pp 129-174, preprint, arxiv.

Equidistribution from fractal measures
With Pablo Shmerkin.
Inventiones Mathematicae Volume 202 (2015), Issue 1, pp 427-479, journal, arxiv.

Self-similar sets, entropy and additive combinatorics
In Geometry and Analysis of Fractals,
Springer Proceedings in Mathematics & Statistics Volume 88, 2014, pp 225-252, book, arxiv, Remark about print version.

On self-similar sets with overlaps and inverse theorems for entropy
Annals of Mathematics 180 (2014), no. 2, 773–822. journal, arxiv.

On the ratio ergodic theorem for group actions
Journal of the London Mathematical Society (2) 88 (2013), no. 2, 465–482 journal, arxiv.

Isomorphism and embedding into Markov shifts off universally null sets
Acta Applicandae Mathematicae, Volume 126 (Hang Kim Memorial Volume), Issue 1 (2013), Page 187-201. journal, arxiv, erratum.

Examples of non-polygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models
With Michael Damron.
Annals of Applied Probability 2013, Vol. 23, No. 3, 1074-1085, journal, arxiv.

Geometric rigidity of times-m invariant measures
Journal of the European Mathematical Society, Volume 14, Issue 5, 2012, pp. 1539–1563, journal, arxiv, erratum.

On the finite-dimensional marginals of shift-invariant measures
With J.-R. Chazottes , J.-M. Gambaudo , and E. Ugalde .
Ergodic Theory and Dynamical Systems, Volume 32, Issue 5, 2012 , pp 1485-1500, journal, arxiv

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

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 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.

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

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

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

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.


Lectures on dynamics, fractal geometry and metric number theory.
Lecture notes frmo the 2011 Bedlewo summer schoold on “Modern Dynamics and its Interaction with Analysis, Geometry and Number Theory”. The notes cover Furstenebrg's theory of CP chains, and applications to intersections and projections of fractals (including Furstenberg's 1970 theorem on intersections of Cantor sets and the Peres-Shmerkin and Hochman-Shmerkin theorems on projections. pdf, journal version.

Notes on information theory (source coding).
These are rough notes from a short (3 lecture) 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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