Papers by Alexander Litvak
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R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Sharp bounds on the rate of convergence of empirical
covariance matrix",
C. R., Math., Acad. Sci. Paris, to appear.
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R. Adamczak, O. Guedon, A. E. Litvak, A. Pajor,
N. Tomczak-Jaegermann,
"Condition number of a square matrix with i.i.d. columns drawn
from a convex body",
Proc. Amer. Math. Soc., to appear,
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Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Uniform estimates for order statistics and Orlicz functions",
Positivity, to appear,
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R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Restricted isometry property of matrices with independent columns
and neighborly polytopes by random sampling",
Constructive Approximation, to appear
(published online 4 August 2010,
DOI: 10.1007/s00365-010-9117-4).
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O. Guedon, A. E. Litvak,
"On the symmetric average of a convex body",
Advances in Geometry, to appear,
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A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann,
"Essentially-Euclidean convex bodies",
Studia Math.,
196 (2010), 207--221.
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R. Adamczak, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Quantitative estimates of the convergence of the empirical
covariance matrix in Log-concave Ensembles",
Journal of AMS,
234 (2010), 535--561.
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K. Bezdek, A. E. Litvak,
"Covering convex bodies by cylinders and lattice points by flats",
Journal of Geometric Analysis,
19 (2009). 233--243.
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R. Adamczak, O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Smallest singular value of random matrices with independent columns",
C. R., Math., Acad. Sci. Paris,
346 (2008), 853--856.
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E. D. Gluskin, A. E. Litvak,
"Asymmetry of convex polytopes and
vertex index of symmetric convex bodies.",
Discrete and Computational Geometry,
40 (2008), 528--536.
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Y. Gordon, A. E. Litvak, S. Mendelson, A. Pajor,
"Gaussian averages of interpolated bodies and applications
to approximate reconstruction",
J. of Approx. Theory,
149 (2007), 59--73.
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K. Bezdek, A. E. Litvak,
"On the vertex index of convex bodies",
Adv. Math.,
215 (2007), 626--641.
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A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann,
"On the Euclidean metric entropy of convex bodies",
GAFA, Lecture Notes in Math., 1910,
221--235, Springer, Berlin, 2007.
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Y. Gordon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Random $\eps$ nets and embeddings in $\ell^N_\infty$",
Stud. Math., 178 (2007), 91--98.
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A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann,
"Entropy extension",
Funct. Anal. Appl., 40 (2006), 298--303.
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Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"On the minimum of several random variables",
Proc. AMS, 134 (2006), 3665--3675.
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A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Diameters of Sections and Coverings of Convex Bodies",
J. of Funct. Anal., 231 (2006), 438--457.
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A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann,
R. Vershynin, "Euclidean embeddings in spaces of finite
volume ratio via random matrices",
J. Reine Angew. Math.,
589 (2005), 1--19.
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A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann,
"Smallest singular value of random matrices and geometry of
random polytopes",
Adv. Math.,
195 (2005), 491--523.
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Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Minima of sequences of Gaussian random variables",
C.R. Acad. Sci. Paris, Ser 1, Math.,
340 (2005), 445--448.
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A. E. Litvak, "On the dual form of "Low M* -estimate"
in the quasi-convex case",
Positivity, 8 (2004), 401--406.
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A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann,
"When random proportional subspaces are also random quotients",
J. of Funct. Anal., 213 (2004), 270--289.
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Y. Gordon, A. E. Litvak, M. Meyer, A. Pajor,
"Jonn's decomposition in the general case and applications",
J. of Diff. Geometry, 68 (2004), 99--119.
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A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann,
"Isomorphic random subspaces and quotients of convex
and quasi-convex bodies",
GAFA, Lecture Notes in Math., 1850,
159--178, Springer-Verlag, 2004.
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A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin,
"Random Euclidean embeddings in spaces of bounded volume ratio",
C.R. Acad. Sci. Paris, Ser 1, Math.,
339 (2004), 33--38.
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A. E. Litvak, V. D. Milman,
"Euclidean sections of direct sums of normed spaces",
Can. Math. Bull.,
46 (2003), 242--251.
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Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Geometry of spaces between zonoids and polytopes",
Bull. Sci. Math.,
126 (2002), 733--762.
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Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Orlicz Norms of Sequences of Random Variables",
Ann. Probab.,
30 (2002), 1833--1853.
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A. E. Litvak, P. Mankiewicz, N. Tomczak-Jaegermann,
"Randomized Isomorphic Dvoretzky Theorem",
C.R. Acad. Sci. Paris, Ser 1, Math.,
335 (2002), 345--350.
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N. J. Kalton, A. E. Litvak,
"A remark on quotients of finite-dimensional quasi-normed spaces",
Houston Journal of Math.,
28 (2002), 585--597.
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E. D. Gluskin, A. E. Litvak,
"On the asymmetry constant of a body with few vertices",
Geometriae Dedicate,
90 (2002), 45--48.
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E. D. Gluskin, A. E. Litvak, N. Tomczak-Jaegermann,
"An example of the body without symmetric projections",
Israel Journal of Math.,
124 (2001), 267--277.
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A. E. Litvak,
"Kahane-Khinchin's inequality for the quasi-norms",
Can. Math. Bull.,
43 (2000), 368--379.
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A. E. Litvak, N. Tomczak-Jaegermann,
"Random aspects of high-dimensional convex bodies",
GAFA, Lecture Notes in Math., 1745, 169--190,
Springer-Verlag, 2000.
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O. Guedon, A. E. Litvak,
"Euclidean projections of p-convex body",
GAFA, Lecture Notes in Math., 1745, 95--108,
Springer-Verlag, 2000.
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W. Banaszczyk, A. E. Litvak, A. Pajor, S. J. Szarek,
"The flatness theorem for non-symmetric convex bodies
via the local theory of Banach spaces",
Math. of Oper. Research.,
24 (1999), 728--750.
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- A. E. Litvak, V. D. Milman, A. Pajor,
"Covering numbers and "low M*-estimate" for quasi-convex bodies",
Proc. Amer. Math. Soc.,
127 (1999), 1499--1507.
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A. E. Litvak,
"On the constant in the reverse Brunn-Minkowski inequality for
p-convex balls",
Convex Geometric Analysis,
(Berkeley, CA, 1996),
129--137,
Math. Sci. Res. Inst.
Publ. V. 34, Cambridge Univ. Press,
Cambridge, 1999.
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A. E. Litvak,
"The extension of the finite-dimensional version
of Krivine's theorem to quasi-normed spaces",
Convex Geometric Analysis,
(Berkeley, CA, 1996),
139--148,
Math. Sci. Res. Inst.
Publ. V. 34, Cambridge Univ. Press,
Cambridge, 1999.
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- A. E. Litvak, V. D. Milman, G. Schechtman,
"Averages of norms and quasi-norms",
Math. Ann.,
312 (1998), 95--124.
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- A. E. Litvak, V. D. Milman, G. Schechtman,
"Averages of norms and behaviour of families of
projective caps on the sphere",
C.R. Acad. Sci. Paris, Ser 1, Math.,
325 (1997), 289--294.
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A. E. Litvak,
"Properties of the operator of discrete integrations and some
applications",
Vestnik St. Petersburg Univ., Math.,
25 (1992), 28--30.
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