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Simultaneous structures in convex signal recovery - revisiting the convex combination of norms.
Frontiers Appl. Math. Stat. 5 (2019), 23 p. DOIArxiv.org eprint 31 p.
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Bound on Bell Inequalities by Fraction of Determinism and Reverse Triangle Inequality.
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Phys. Rev. A. 90, 012301 (2014).
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Phase transitions for random states and a semicircle law for the partial transpose.
Phys. Rev. A. 85, 030302(R) (2012).
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Concentration for noncommutative polynomials in random matrices.
Proc. Amer. Math. Soc. 140, No. 5 (2012), 1803-1813.
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(with M. Meckes)
On some convexity properties of the Least Squares Method for
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How often is a random quantum state k-entangled?
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Hastings's additivity counterexample via Dvoretzky's theorem.
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Almost-Euclidean subspaces of $\ell_1^N$ via tensor products: a simple approach to randomness reduction.
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Non-additivity of Rényi entropy and Dvoretzky's theorem.
J. Math. Phys. 51, 022102 (2010). Arxiv.org eprint 8 p.
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On the nontrivial projection problem.
Advances in Math. 221 (2009), 331-342.
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Geometry of sets of quantum maps: a generic positive map acting
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Convexity, Complexity, and High Dimensions.
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J. Phys. A: Math. Gen. 39 (2006) L119-L126.
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Tensor products of convex sets and the volume of separable states on N qudits.
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Saturating Constructions for Normed Spaces II. J. Funct. Anal. 221 (2005), no. 2, 407-438.
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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.
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Saturating Constructions for Normed Spaces. Geom. Funct. Anal. 14 (2004), no. 6, 1352-1375.
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Duality of metric entropy in euclidean space.
C. R. Acad. Sci. Paris. 337 (2003), no. 11, 711-714.
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On Gram matrices of uniformly bounded systems of functions.
Trudy MIAN 243 (2003), 237-243 (English transl. Proc. Steklov Inst.
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The Knaster problem and the geometry of high-dimensional cubes.
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More on the Duality Conjecture for Entropy Numbers.
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On the geometry of proportional quotients of ${l^m_1}$}.
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An Analysis of Completely-Positive Trace-Preserving
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A Geometric Approach to Duality of Metric Entropy.
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Shannon's Entropy Power Inequality via Restricted Minkowski Sums.
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A Geometric Lemma and Duality of Entropy Numbers.
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The Flatness Theorem for Nonsymmetric Convex Bodies
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Random Banach Spaces.The limitations of the method,
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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 recommendations expressed
therein are those of the author(s) and do not necessarily reflect
the views of the NSF.
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