Research interests: Ergodic Theory and its connections with Arithmetic, Commutative Algebra, Harmonic Analysis,
Operator Algebras and Probability Theory.
Positive definite kernels, continuous tensor products, and central limit theorems in probability theory (with K. R. Parthasarathy). Lecture Notes in Mathematics, Vol. 272, Springer Verlag 1972.
Cocycles of ergodic transformation groups. Lecture Notes in Mathematics, Vol. 1, MacMillan (India) 1977. PDF (Warning: 10 MB)
Dynamical systems of algebraic origin. Progress in Mathematics, Vol. 128, Birkhäuser Verlag 1995.
Algebraic Zd-actions. Pacific Institute for the Mathematical Sciences Distinguished Chair Lecture Notes, University of Victoria, BC, November 2002. 60pp. (electronic publication). PDF
Ergodentheorie und Topologische Dynamik. (with M. Einsiedler). Birkhäuser Verlag, Basel, 2014. viii+159 pp.
Edited Conference Proceedings
Ergodic Theory of Zd-actions: Proceedings of the Warwick Symposium 1993/94 (joint editor with M. Pollicott). London Mathematical Society Lecture Notes, Vol. 228, Cambridge University Press 1996.
Random Walks and Geometry: Proceedings of a Workshop at the Erwin Schrödinger Institute, June 18 - July 13, 2001 (joint editor with V. Kaimanovich (Principal Editor) and W. Woess). De Gruyter, Berlin-New York, 2004.
Diophantine Approximation: Festschrift for Wolfgang Schmidt (joint editor with H.P. Schlickewei (Principal Editor) and R. Tichy). Springer Verlag, Wien-New York, 2008.
Articles
Ergodicity of principal algebraic group actions (with H. Li and J. Peterson), to appear in Contemp. Math.PDF
Homoclinic points and atoral polynomials (with D. Lind and E. Verbitskiy), Ergod. Th. amp; Dynam. Sys.33 (2013), 1060--1081. PDF
Ergodic Theory and Number Theory: The Work of Elon Lindenstrauss. Internat. Math. Nachr.216 (2011), 1--13. PDF
Entropy and growth rate of periodic points of algebraic Zd-actions (with D. Lind and E. Verbitskiy), in: Dynamical Numbers: Interplay between Dynamical Systems and Number Theory, Contemp. Math., vol. 532, American Mathematical Society, Providence, R.I., 2010, 195--211. PDF
Abelian sandpiles and the harmonic model (with E. Verbitskiy). Comm. Math. Phys.292 (2009), 721--759. PDF
Expansive algebraic actions of discrete residually finite amenable groups and their entropy (with C. Deninger). Ergod. Th. & Dynam. Sys.27 (2007), 769-786. PDF
Quotients of l\infty (Z,Z) and symbolic covers of toral automorphisms. Amer. Math. Soc. Transl.217 (2006), 223-246. PDF
Recurrence of cocycles and stationary random walks. In: Dynamics & Stochastics: Festschrift in Honor of M. S. Keane, ed. Dee Denteneer, Frank den Hollander and Evgeny Verbitskiy, IMS Lecture Notes - Monograph Series, vol. 48, Institute of Mathematical Statsistics, Beachwood, Ohio, 2006, 78-84. PDF
Symbolic representations of nonexpansive group automorphisms (with E. Lindenstrauss). Israel J. Math.149 (2005), 227-266. PDF
Algebra, arithmetic and multi-parameter ergodic theory. Internat. Math. Nachrichten200 (2005), 1-21. PDF
Invariant measures of nonexpansive group automorphisms (with E. Lindenstrauss). Israel J. Math.144 (2004), 29-60. PDF
Algebraic Zd-actions on zero-dimensional compact abelian groups. In: Modern Dynamical Systems and Applications, ed. M. Brin, B. Hasselblatt and Ya. Pesin, Cambridge University Press, Cambridge, 2004, 185-209. PDF
Homoclinic points and isomorphism rigidity of algebraic Zd-actions on zero-dimensional compact abelian groups (with S. Bhattacharya). Israel J. Math.137 (2003), 189-209. PDF
Growth and recurrence of stationary random walks (with G. Greschonig). Probab. Theor. Relat. Fields125 (2003), 266-270. PDF
Affinely infinitely divisible distributions and the embedding problem (with S.G. Dani). Math. Res. Lett.9 (2002), 607-620. PDF Correction, 12 (2005), 817-820. PDF
Rigidity of measurable structure for algebraic actions of higher-rank abelian groups (with A. Katok and S. Katok). Comment. Math. Helv.77 (2002), 718-745. PDF
Dispersing cocycles and mixing flows under functions. Fund. Math.173 (2002), 191-199. PDF
Irreducibility, homoclinic points and adjoint actions of algebraic Zd-actions of rank one (with M. Einsiedler). In: Nonlinear Phenomena and Complex Systems, ed. A. Maass, S. Martinez and J. San Martin, Kluwer Academic Publishers, Dordrecht, 2002, 95-124. PDF
The adjoint action of an expansive algebraic Zd-action (with M. Einsiedler). Mh. Math.135 (2002), 203-220. PDF
Invariant cocycles have abelian ranges (with G. Greschonig). Mh. Math.134 (2002), 207-216. PDF
Symbolic and algebraic dynamical systems (with D. Lind). In: Handbook of Dynamical Systems, ed. B. Hasselblatt and A. Katok, vol. 1A, North Holland, Amsterdam, 2002, 765-812. PDF
Measurable rigidity of algebraic Zd-actions. In: Smooth Ergodic Theory and its Applications, Proceedings of Symposia in Pure Mathematics, vol. 69, American Mathematical Society, Providence, R.I., 2001, 661-676. PDF
The dynamics of algebraic Zd-actions. In: European Congress of Mathematics Barcelona 2000, Vol. I, ed. C. Casacuberta, R.M. Miró-Roig, J. Verdera and S. Xambó-Descamps, Progress in Mathematics, vol. 201, Birkhäuser Verlag, Basel-Berlin-Boston, 2001, 543-553. PDF
Multi-dimensional symbolic dynamical systems. In: Codes, Systems and Graphical Models, ed. B. Marcus and J. Rosenthal, IMA Volumes in Mathematics and its Applications, vol. 123, 2001, 67-82. PDF
Isomorphism rigidity of irreducible algebraic Zd-actions (with B. Kitchens). Inventiones math.142 (2000), 559-577. PDF
Ergodic decomposition of quasi-invariant probability measures (with G. Greschonig). Coll. Math.84/85 (2000), 495-514. PDF
Algebraic coding of expansive group automorphisms and two-sided beta-shifts. Mh. Math.129 (2000), 37-61. PDF
Common homoclinic points of commuting toral automorphisms (with A. Manning), Israel J. Math.114 (1999), 289-299. PDF
Tail-fields of products of random variables and ergodic equivalence relations. Ergod. Th. & Dynam. Sys.19 (1999), 1325-1341. PDF
Homoclinic points of algebraic Zd-actions (with D. Lind). J. Amer. Math. Soc.12 (1999), 953-980. PDF
Remarks on Livsic' theory for nonabelian cocycles. Ergod. Th. & Dynam. Sys.19 (1999), 703-721. PDF
On joint recurrence, C. R. Acad. Sci. Paris Sér. I Math.327 (1998), 837-842. PDF
Tilings, fundamental cocycles and fundamental groups of symbolic Zd-actions. Ergod. Th. & Dynam. Sys.18 (1998), 1473-1525. PDF
On the cohomology of algebraic Zd-actions with values in compact Lie groups. In: Lie Groups and Ergodic Theory (Proceed. of Internat. Colloq. at the Tata Institute, Mumbai 1996), ed. S.G. Dani, Narosa Publishing House, New Delhi, 1998, 203-228. PDF
Markov partitions and homoclinic points of algebraic Zd-actions (with M. Einsiedler). Proc. Steklov Inst. Math.216 (1997), 259-279. PDF
Invariant cocycles, random tilings and the super-K and strong Markov properties. Trans. Amer. Math. Soc.349 (1997), 2812-2825. PDF
Symmetric Gibbs measures (with K. Petersen). Trans. Amer. Math. Soc.349 (1997), 2775-2811. PDF
Extensions of cocycles for hyperfinite actions and applications (with P. Gabriel and M. Lema\'nczyk). Mh. Math.123 (1997), 209-228.
From infinitely divisible representations to cohomological rigidity. In: Analysis, Geometry and Probability, ed. R. Bhatia and A.G. Bhatt, Hindustan Book House, Delhi 1996, pp. 173-197. PDF
Almost block independence and Bernoullicity of Zd-actions by automorphisms of compact groups (with D. Rudolph). Inventiones math.120 (1995), 455-488.
Associated actions and uniqueness of cocycles (with J. Aaronson and T. Hamachi). In: Algorithms, Fractals and Dynamics, ed. Y. Takahashi, Plenum Publishing Company, New York 1996, 1-25.
Invariant measures for certain expansive Z2-actions. Israel J. Math.90 (1995), 295-300.
The cohomology of higher-dimensional shifts of finite type. Pacific J. Math.170 (1995), 237-270.
