My Publication (last update Jun. 16, 2020)

Please note: for papers which have already appeared, the version of the paper below may be less up to date than the published one.

  1. Lowering Topological Entropy, J. D'Analyse Math. 67, 1995, pp 231--267
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  2. Measurable Distal and Topological Distal Systems, Ergod. Th. & Dynam. Systems Vol. 19 (1999), pp 1063--1076
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  3. Entropy and Convolutions on the Circle, with D. Meiri and Y. Peres, Ann. of Math. Vol. 149 (1999), pp. 871--904
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  4. Indistinguishable Sceneries, Rand. Struc. & Algorithms Vol. 14 (1999), No. 1, pp. 71--86
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  5. Mean Topological Dimension, with B. Weiss, Israel J. of Math. Vol. 115 (2000), pp. 1--24
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  6. Mean Dimension, Small Entropy Factors, and an Embedding Theorem, Publ. Math. IHES no. 89 (1999) pp. 227--262
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  7. On Sets Invariant under the Action of the Diagonal Group, with Barak Weiss, Ergodic Theory Dynam. Systems 21 (2001), no. 5, 1481--1500.
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  8. Pointwise Theorems for Amenable Groups (research announcement), Electronic Research Announcements of the AMS, 1999, vol. 5, pp. 82--90.
  9. Pointwise Theorems for Amenable Groups, Invent. Math. 146 (2001), no. 2, 259--295.
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  10. $p$-adic Foliations and Equidistribution, Israel J. Math. 122 (2001), 29--42.
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  11. Bernoulli convolutions and an intermediate value theorem for entropy of K-partitions, with Yuval Peres and Wilhelm Schlag, J. d'Analyse Math 87 (2002), 337-367.
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  12. On quantum unique ergodicity for $\Gamma\backslash\H\times\H$, Internat. Math. Res. Notices 2001, no. 17, 913--933.
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    Corrections: PostScript DVI PDF
  13. Entropy of Quantum Limits, with Jean Bourgain, Comm. Math. Phys. 233 (2003), no. 1, 153--171.
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    Corrections and additions: DVI PDF
  14. On the projections of measures invariant under the geodesic flow, with Francois Ledrappier, Internat. Math. Res. Notices 2003, no. 9, 511-526.
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  15. Rigidity properties of Z^d-actions on tori and solenoids, with Manfred Einsiedler
    Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 99-110.
  16. On Fractal Measures and Diophantine Approximation, with Dmitry Kleinbock and Barak Weiss, Selecta Math., 10:479--523, 2004.
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  17. Invariant sets and measures of nonexpansive group automorphisms, with Klaus Schmidt, Israel J. Math., 144:29--60, 2004.
    DVI PDF
  18. Rigidity of multiparameter actions (survey paper). Israel J. Math., 149:199--226, 2005.
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  19. Symbolic representations of nonexpansive group automorphisms, with Klaus Schmidt Israel J. Math., 149:227--266, 2005
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  20. Invariant measures and arithmetic quantum unique ergodicity, Ann. of Math. (2), 163(1):165--219, 2006.
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  21. Invariant measures and the set of exceptions to Littlewoods conjecture, with Manfred Einsiedler and Anatole Katok, Ann. of Math. (2), 164(2):513--560, 2006.
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  22. Existence and Weyl's law for spherical cusp forms, with Akshay Venkatesh, Geom. Funct. Anal., 17(1):220--251, 2007.
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  23. Arithmetic quantum unique ergodicity and adelic dynamics. In the proceedings of Current Developments in Mathematics conference, Harvard 2004 (30 pages), 2005.
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  24. Invariant measures for multiparameter diagonalizable algebraic actions---a short survey. In European Congress of Mathematics, pages 247--256. Eur. Math. Soc., Z\"urich, 2005.
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  25. Joining of higher rank diagonalizable actions on locally homogeneous spaces, with Manfred Einsiedler, Duke Math. J., 138(2):203--232, 2007.
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  26. Diagonal flows on locally homogeneous spaces and number theory, with Manfred Einsieder. In International Congress of Mathematicians. Vol. II, pages 1731--1759. Eur. Math. Soc., Z\"urich, 2006.
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  27. The distribution of periodic torus orbits on homogeneous spaces, with Manfred Einsiedler, Philippe Michel, and Akshay Venkatesh. Duke Math. J. 148 (2009), no. 1, 119--174.
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  28. Some examples how to use measure classification in number theory. In Equidistribution in number theory, an introduction, volume 237 of NATO Sci. Ser. II Math. Phys. Chem., pages 261--303. Springer, Dordrecht, 2007.
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  29. Ergodic theory of the space of measured laminations, with Maryam Mirzakhani, Int. Math. Res. Not. (4) 2008, 49 pp.
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  30. Distribution of periodic torus orbits and Duke's theorem for cubic fields, with Manfred Einsiedler, Philippe Michel, and Akshay Venkatesh. Ann. of Math. (2) 173 (2011), no. 2, 815--885.
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  31. On measures invariant under diagonalizable actions – the rank one case and the general low entropy method, with Manfred Einsiedler. Journal of Modern Dynamics, 2(1):83--128, 2008.
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  32. Invariant measures and stiffness for non-abelian groups of toral automorphisms, with Jean Bourgain, Alex Furman, and Shahar Mozes. C. R. Math. Acad. Sci. Paris, 344(12):737--742, 2007.
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  33. Some effective results for $\times a, \times b$, with Jean Bourgain, Philippe Michel, and Akshay Venkatesh. Ergodic Theory Dynam. Systems 29 (2009), no. 6, 1705–1722.
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  34. Diagonal actions on locally homogeneous spaces, with Manfred Einsiedler. In Homogeneous flows, moduli spaces and arithmetic, 155–241, Clay Math. Proc., 10, Amer. Math. Soc., Providence, RI, 2010.
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  35. Stationary measures and equidistribution for orbits of non-abelian semigroups on the torus, with Jean Bourgain, Alex Furman, and Shahar Mozes. J. Amer. Math. Soc., 24(1):231--280, 2011.
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  36. Non-localization of eigenfunctions on large regular graphs, with Shimon Brooks. Israel J. Math., 193(1):1--14, 2013.
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  37. Homogeneous orbit closures and applications, with Uri Shapira. Ergodic Theory Dynam. Systems, 32(2):785--807, 2012.
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  38. Graph eigenfunctions and quantum unique ergodicity, with Shimon Brooks. Comptes Rendus Mathematique, Volume 348, Issues 15-16, August 2010, Pages 829-834.
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  39. Equidistribution in homogeneous spaces and number theory. Proceedings of the International Congress of Mathematicians, Hyderabad 2010.
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  40. The distribution of closed geodesics on the modular surface, and Duke's theorem, with Manfred Einsiedler, Philippe Michel, and Akshay Venkatesh. Enseign. Math. (2), 58(3-4):249–313, 2012.
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  41. Topological self-joinings of Cartan actions by toral automorphisms, with Zhiren Wang. Duke Math. J., 161(7):1305--1350, 2012.
    arXiv
  42. Joint quasimodes, positive entropy, and quantum unique ergodicity, with Shimon Brooks. Invent. Math., 198(1):219--259, 2014.
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  43. Mean dimension and an embedding problem: an example, with Masaki Tsukamoto. Israel Journal of Mathematics, pages 1--12, 2013.
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  44. On measures invariant under tori on quotients of semi-simple groups, with Manfred Einsiedler. Ann. of Math. (2) 181 (2015), no. 3, 993--1031.
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  45. Hausdorff dimension and subgroups of {$SU(2)$}, with Nicolas de Saxc\'e. Israel J. Math. 209 (2015), no. 1, 335--354.
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  46. Effective estimates on indefinite ternary forms, with Gregory Margulis. Israel J. Math. 203 (2014), no. 1, 445--499.
    Dedicated to the memory of my father, Joram Lindenstrauss
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  47. Singular systems of linear forms and non-escape of mass in the space of lattices, with Shiraly Kadyrov, Dmitry Kleinbock and Gregory Margulis. J. Anal. Math. 133 (2017), 253--277. arXiv:1407.5310
  48. Random walks in the group of euclidean isometries and self-similar measures, with Peter Varju. Duke Math. J. 165 (2016), no. 6, 1061--1127.
    arXiv:1405.4426
  49. Spectral gap in the group of affine transformations over prime fields, with Peter Varju. Ann. Fac. Sci. Toulouse Math. (6) 25 (2016), no. 5, 969--993.
    arXiv:1409.3564
  50. Joinings of higher rank torus actions on homogeneous spaces, with Manfred Einsiedler. Publ. Math. Inst. Hautes Etudes Sci. 129 (2019), 83--127.
    arXiv:1502.05133
  51. Quantum Ergodicity and Averaging Operators on the Sphere, with Shimon Brooks and Etienne Le Masson. Int. Math. Res. Not. IMRN 2016, no. 19, 6034--6064.
    arXiv:1505.03887
  52. Mean dimension of Z^k-actions, with Yonatan Gutman and Masaki Tsukamoto. Geom. Funct. Anal. 26 (2016), no. 3, 778--817.
    arXiv:1510.01605
  53. From rate distortion theory to metric mean dimension: variational principle, with Masaki Tsukamoto. IEEE Trans. Inform. Theory 64 (2018), no. 5, 3590--3609.
    arxiv:1702.05722
  54. Diagonal actions in positive characteristic, with M. Einsiedler and A. Mohammadi. Duke Math. J. 169 (2020), no. 1, 117--175.
    arxiv:1705.10418
  55. Symmetry of entropy in higher rank diagonalizable actions and measure classification, with M. Einsiedler. J. Mod. Dyn. 13 (2018), 163--185.
    arXiv:1803.07762
  56. Double variational principle for mean dimension, with M. Tsukamoto. Geom. Funct. Anal. 29 (2019), no. 4, 1048--1109.
    arXiv:1901.05623
  57. Quantitative behavior of unipotent flows and an effective avoidance principle, with A. Mohammadi, G. A. Margulis, and N. Shah. submitted (52pp).
    arXiv:1904.00290
  58. On Radon measures invariant under horospherical flows on geometrically infinite quotients, with Or Landesberg.
    arXiv:1910.08956
  59. Affine random walks on the torus, with Weikun He and Tsviqa Lakrec. submitted (23pp).
    arXiv:2003.0374
  60. Recent progress on rigity properties of higher rank diagonalizable actions and applications. A survey to appear in a volume dedicated to G. A. Margulius.
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