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*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)*Entanglement thresholds for random induced states.*Comm. Pure Appl. Math., to appear. Arxiv.org eprint 34 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. 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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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Some of the above materials are based upon work supported by grants from the National Science Foundation. Any opinions, findings and conclusions or recomendations expressed therein are those of the author(s) and do not necessarily reflect the views of the NSF.

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