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*Bound entangled states with extremal properties.*To appear in Phys. Rev. A. Arxiv.org eprint 8 p. (with P. Baciag, K. Horodecki, M. Horodecki and J. Jenkinson)*Entanglement thresholds for random induced states.*Comm. Pure Appl. Math. 67 (2014), 129-171. Arxiv.org eprint 34 p. (with G. Aubrun and D. Ye)*Phase transitions for random states and a semicircle law for the partial transpose.*Phys. Rev. A. 85, 030302(R) (2012). Arxiv.org eprint 5 p. (with G. Aubrun and D. Ye)*Concentration for noncommutative polynomials in random matrices.*Proc. Amer. Math. Soc. 140, No. 5 (2012), 1803-1813. Arxiv.org eprint 11 p. (with M. Meckes)*On some convexity properties of the Least Squares Method for pairwise comparisons matrices without the reciprocity condition.*J. Global Optim. 54 (2012), no. 4, 689-706. Journal Website (with J. Fülöp and W. W. Koczkodaj)*How often is a random quantum state k-entangled?*J. Phys. A: Math. Theor. 44, 045303 (2011). Arxiv.org eprint 19 p. (with E. Werner and K. Zyczkowski)*Hastings's additivity counterexample via Dvoretzky's theorem.*Comm. Math. Physics 305, 85-97 (2011). Arxiv.org eprint 12 p. (with G. Aubrun and E. Werner)*Almost-Euclidean subspaces of $\ell_1^N$ via tensor products: a simple approach to randomness reduction.*In "APPROX and RANDOM 2010," M. Serna et al (Eds.) LNCS 6302, Springer-Verlag Berlin Heidelberg 2010, 632-641. Arxiv.org eprint 11 p. (with P. Indyk)*Non-additivity of Rényi entropy and Dvoretzky's theorem.*J. Math. Phys. 51, 022102 (2010). Arxiv.org eprint 8 p. (with G. Aubrun and E. Werner)*On the nontrivial projection problem.*Advances in Math. 221 (2009), 331-342. Arxiv.org eprint 17 p. (with N. Tomczak-Jaegermann)*On norms of completely positive maps.*In "Proceedings of IWOTA 2008", Oper. Theory Adv. Appl. Vol. 202, Birkhauser, Basel 2010, 535-538. Arxiv.org eprint 2 p.*Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive.*J. Math. Phys. 49, 032113 (2008) Arxiv.org eprint 34 p. (with E. Werner and K. Zyczkowski)*Convexity, Complexity, and High Dimensions.*In "Proceedings of the International Congress of Mathematicians (Madrid, 2006)," Vol. II. European Math. Soc. 2006, 1599-1621. Available online from icm2006.org*Decoupling weakly dependent events.*In "Geometric Aspects of Functional Analysis, Israel Seminar 2004-2005", V.D. Milman and G. Schechtman eds., Lecture Notes in Math. 1910, Springer Verlag, Berlin 2007, 297-303. Preprint in PDF format, 8 p. (with N. Tomczak-Jaegermann)*On the structure of the body of states with positive partial transpose.*J. Phys. A: Math. Gen. 39 (2006) L119-L126. Arxiv.org eprint 10 p. (with I. Bengtsson and K. Zyczkowski)*Tensor products of convex sets and the volume of separable states on N qudits.*Phys. Rev. A. 73, 022109 (2006). Arxiv.org eprint 14 p. (with G. Aubrun)*The volume of separable states is super-doubly-exponentially small in the number of qubits.*Phys. Rev. A 72, 032304 (2005). Arxiv.org eprint 20 p.*Saturating Constructions for Normed Spaces II.*J. Funct. Anal. 221 (2005), no. 2, 407-438. Preprint in PDF format, 35 p. (with N. Tomczak-Jaegermann)*On convexified packing and entropy duality.*Geom. Funct. Anal. 14 (2004), no. 5, 1134-1141. Preprint in PDF format, 6p. (with S. Artstein, V. Milman and N. Tomczak-Jaegermann)*Duality of Metric Entropy.*Annals of Math. 159 (2004), no. 3, 1313-1328. Preprint in PDF format, 17 p. (with S. Artstein and V. Milman)*Saturating Constructions for Normed Spaces.*Geom. Funct. Anal. 14 (2004), no. 6, 1352-1375. Preprint in PDF format, 27 p. (with N. Tomczak-Jaegermann)*Duality of metric entropy in euclidean space.*C. R. Acad. Sci. Paris. 337 (2003), no. 11, 711-714. Preprint in English in PDF format, 5 p. (with S. Artstein and V. Milman)*On Gram matrices of uniformly bounded systems of functions.*Trudy MIAN 243 (2003), 237-243 (English transl. Proc. Steklov Inst. 243 (2003), 227--233.) Preprint in Russian in PDF format, 10 p. English transl. (with B.S. Kashin)*The Knaster problem and the geometry of high-dimensional cubes.*C. R. Acad. Sci. Paris Sér. I Math. 336 (2003), no. 11, pp. 931--936. Preprint in English in PDF format, 6 p. (with B. S. Kashin)*More on the Duality Conjecture for Entropy Numbers.*C. R. Acad. Sci. Paris Sér. I Math. 336 (2003), no. 6, 479--482. (with S. Artstein and V. Milman)*On the geometry of proportional quotients of ${l^m_1}$}.*Studia Math. 155 (2003), 51--66. Preprint in PDF format, 19 p. (with P. Mankiewicz)*An Analysis of Completely-Positive Trace-Preserving Maps on $M_2$.*Linear Algebra Appl. 347 (2002), 159--187. Arxiv.org eprint (with M.B. Ruskai and E. Werner)*A Geometric Approach to Duality of Metric Entropy.*C. R. Acad. Sci. Paris Sér. I Math. 332 (2001), no. 2, 157-162. Preprint in PDF format (with V. Milman)*Shannon's Entropy Power Inequality via Restricted Minkowski Sums.*In "Geometric Aspects of Functional Analysis", V.D. Milman and G. Schechtman eds., Lecture Notes in Math. 1745, Springer Verlag, Berlin 2000, 257-262. Preprint in PDF format (with D. Voiculescu)*Local operator theory, random matrices and Banach spaces.*In "Handbook on the Geometry of Banach spaces," Volume 1, W.B. Johnson, J. Lindenstrauss eds., Elsevier Science 2001, pp. 317-366. Addenda and Corrigenda, in Volume 2, 2003, pp. 1819-1820. Preprint in PDF format, 59 p. Addenda and Corrigenda, 2 p. (with K.R. Davidson)*A Geometric Lemma and Duality of Entropy Numbers.*In "Geometric Aspects of Functional Analysis, Israel Seminar 1996-2000", V.D. Milman and G. Schechtman eds., Lecture Notes in Math. 1745, Springer Verlag, Berlin 2000, 191-222. Preliminary version: Erwin Schroedinger Institute, Vienna, preprint # 687, April 1999, 40 p., available via http://www.esi.ac.at/preprints/ESI-Preprints.html (with V. Milman)*The Flatness Theorem for Nonsymmetric Convex Bodies via the Local Theory of Banach Spaces,*Math. of Operation Research 24 (1999), no. 3, 728-750 preprint (with W. Banaszczyk, A.E. Litvak and A. Pajor)*Non-symmetric Correlation Inequality for Gaussian Measure,*J. Multivariate Analysis 68 (1999), 193-211 Arxiv.org eprint (with E. Werner)*Metric entropy of homogeneous spaces,*Quantum Probability (Gdansk, 1997), 395-410, Banach Center Publ. 43, Polish Acad. Sci., Warsaw, 1998 Arxiv.org eprint*Lattice coverings and Gaussian measures of n-dimensional convex bodies,*J. of Discrete and Comp. Geom. 17 (1997), 283-286 abstract (with W. Banaszczyk)*On the convexified Sauer-Shelah theorem,*J. Combinatorial Th. B, 69 No.2 (1997), 183-192 preprint in AMSTeX abstract (with M. Talagrand)*Restricted Minkowski sums and the noncommutative entropy power inequality,*Comm. Math. Physics 178 (1996), 563-570 Arxiv.org eprint (with D.Voiculescu)*Random Banach Spaces.The limitations of the method,*Mathematica 41 (1994), pp.239-250 Arxiv.org eprint Corrigenda 42 (1995), pp.220-221 (with P.Mankiewicz)*Condition number of random matrices,*J. Complexity 7 (1991), 131-149*An "isomorphic" version of the Sauer-Shelah lemma and the Banach-Mazur distance to the cube,*GAFA Israel Funct. Anal. Sem., J. Lindenstrauss, V.D. Milman eds., Lecture Notes in Math. vol.1376 Springer Verlag 1989, 105-112 (with M. Talagrand)*On the duality problem for entropy numbers of operators,*as above, 50-63 (with J. Bourgain, A. Pajor and N. Tomczak-Jaegermann)*Spaces with large distance to $l^\infty$ and random matrices,*Amer.J.Math. 112 (1990), 899-942*The Banach-Mazur distance to the cube and the Dvoretzky-Rogers factorization,*Israel J.Math 62 (1988), 169-180 (with J. Bourgain)*An exotic quasidiagonal operator,*J. Funct. Anal. 89 (1990),274-290*On almost commuting Hermitian matrices,*Rocky Mts.J.Math. 20 (1989), 581-589*A Banach space without a basis which has the bounded approximation property,*Acta Math. 159 (1987), 81-98*On the existence and uniqueness of complex structure and spaces with "few" operators,*Trans. A.M.S. 29 (1986), 339-353*How well can an nxn matrix be approximated by reducible ones?*Duke Math.J. 53 (1986), 233-248 (with D. Herrero)*Nets of Grassmann manifold and orthogonal groups*, Proceedings of Banach Space Workshop, University of Iowa Press 1982, 169-185 reprint-
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*Remarks on fixed point problem for nonexpansive mappings,*(in*Fixed points and Nonexpansive Mapings*), A.M.S. 1983, 87-120 (with J. Elton, P.K. Lin and E. Odell) -
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*On the best constant in the Khinchine inequality,*Studia Math. 58 (1976), 197-208

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