- A. E. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, "Small ball probability for the condition number of random matrices," submitted. PDF.
- O. Guedon, A. E. Litvak, K. Tatarko,
"Random polytopes obtained by matrices with heavy tailed entries,"
*Commun. Contemp. Math.,*to appear. PDF. - A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef, "Circular law for sparse random regular digraphs," submitted. PDF.
- A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"Structure of eigenvectors of random regular digraphs,"
*Trans. Amer. Math. Soc.,*to appear. PDF. - A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"The smallest singular value of a shifted $d$-regular random square matrix,"
*Prob. Th. Rel. Fields,*to appear. PDF. - A. E. Litvak, K. Tikhomirov,
"Order statistics of vectors with dependent coordinates,
and the Karhunen--Loeve basis,"
*Annals of Applied Prob.*,**28**(2018), 2083--2104. PDF. - A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"The rank of random regular digraphs of constant degree,"
*J. of Complexity,***48**(2018), 103--110. PDF. - A. E. Litvak,
"Around the simplex mean width conjecture,"
*Analytic Aspects of Convexity, Springer INdAM Series,***25**(2018), 73--84. PDF, PS. - A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"Adjacency matrices of random digraphs: singularity and anti-concentration,"
*J. of Math. Analysis and Appl.,***445**(2017), 1447--1491. Winner of 2017 JMAA Ames Award . PDF, PS. - A. E. Litvak, K. Tikhomirov,
"Estimates for order statistics in terms of quantiles,"
*Zapiski Nauchnykh Seminarov POMI,***457**(2017), 265--275; English translation:*Journal of Math. Sciences,*to appear. PDF, PS. - O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"On the interval of fluctuation of the singular values of random matrices,"
*Journal of the European Mathematical Society,***19**(2017), 1469--1505. PDF, PS. - O. Guedon, A. Hinrichs, A. E. Litvak, J. Prochno,
"On the expectation of operator norms of random matrices,"
*GAFA, Lecture Notes in Math.,***2169**(2017), 151--162. PDF. - K. Bezdek, A. E. Litvak, "Packing convex bodies by cylinders,"
*Discrete and Computational Geometry,***55**(2016), 725--738. PDF, PS. - D. Alonso-Gutierrez, A. E. Litvak,
N. Tomczak-Jaegermann,
"On the isotropic constant of random polytopes,"
*Journal of Geometric Analysis,***26**(2016), 645--662. PDF, PS. - A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"Anti-concentration property for random digraphs and invertibility of their adjacency matrices,"
*C.R. Math. Acad. Sci. Paris,***354**(2016), 121--124. PDF, PS, Offprint - Z. Kabluchko, A. E. Litvak, D. Zaporozhets,
"On the expected maximum of correlated Gaussian variables,"
*Zapiski Nauchnykh Seminarov POMI,***442**(2015), 75--96; English translation:*Journal of Math. Sciences,***225**(2017), 770--787. PDF. - A. E. Litvak, M. Rudelson, N. Tomczak-Jaegermann,
"On approximation by projections of polytopes with few facets,"
*Israel Journal of Math.,***203**(2014), 141--160. PDF, PS. - A. E. Litvak, S. Spektor,
"Quantitative version of a Silverstein's result,"
*GAFA, Lecture Notes in Math.,***2116**(2014), 335--340. PDF, PS. - B. Collins, P. Gawron, A. E. Litvak, K. Zyczkowski,
"Numerical range for random matrices,"
*J. of Math. Analysis and Appl.,***418**(2014), 516--533. PDF - O. Guedon, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Restricted isometry property for random matrices with heavy
tailed columns,"
*C.R. Math. Acad. Sci. Paris,***352**(2014), 431--434. PDF, PS. - R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Tail estimates for norms of sums of log-concave random vectors,"
Proc. London Math. Soc.,
**108**(2014), 600--637. PDF, PS. - R. Adamczak, R. Latala, A. E. Litvak, K. Oleszkiewicz,
A. Pajor, N. Tomczak-Jaegermann,
"A short proof of Paouris' inequality,"
*Canadian Math. Bull,***57**(2014), 3--8. PDF, PS. - R. Adamczak, O. Guedon, R. Latala, A. E. Litvak, K. Oleszkiewicz,
A. Pajor, N. Tomczak-Jaegermann,
"Moment estimates for convex measures,"
*Electron. J. Probab.,***17**no. 101 (2012), 1--19. PDF, PS. - A. E. Litvak, O. Rivasplata,
"Smallest singular value of sparse random matrices,"
*Stud. Math.,***212**(2012), 195--218. PDF, PS. - R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Chevet type inequality and norms of submatrices,"
*Studia Math.,***210**(2012), 35--56. PDF, PS. -
E. D. Gluskin, A. E. Litvak,
"A remark on vertex index of the convex bodies,"
*GAFA, Lecture Notes in Math.,***2050**, 255--265, Springer, Berlin, 2012. PDF, PS. -
Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Uniform estimates for order statistics and Orlicz functions,"
*Positivity,***16**(2012), 1--28. PDF, PS. -
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.,***140**(2012), 987--998. PDF, PS. -
O. Guedon, A. E. Litvak,
"On the symmetric average of a convex body,"
*Advances in Geometry,***11**(2011), 615--622. PDF, PS. - R. Adamczak, R. Latala, A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Geometry of log-concave Ensembles of random matrices and approximate reconstruction,"
*C.R. Math. Acad. Sci. Paris,***349**(2011), 783--786. PDF, PS. -
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,***349**(2011), 195--200. PDF, PS. -
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,***34**(2011), 61--88. PDF, PS. -
A. E. Litvak, V. D. Milman, N. Tomczak-Jaegermann,
"Essentially-Euclidean convex bodies,"
*Studia Math.,***196**(2010), 207--221. PDF, PS. -
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. PDF, PS. -
K. Bezdek, A. E. Litvak,
"Covering convex bodies by cylinders and lattice points by flats,"
*Journal of Geometric Analysis,***19**(2009). 233--243. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
K. Bezdek, A. E. Litvak,
"On the vertex index of convex bodies,"
*Adv. Math.,***215**(2007), 626--641. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
A. E. Litvak, V. D. Milman, A. Pajor, N. Tomczak-Jaegermann,
"Entropy extension,"
*Funct. Anal. Appl.,***40**(2006), 298--303. PDF, PS. -
Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"On the minimum of several random variables,"
*Proc. AMS,***134**(2006), 3665--3675. PDF, PS. -
A. E. Litvak, A. Pajor, N. Tomczak-Jaegermann,
"Diameters of Sections and Coverings of Convex Bodies,"
*J. of Funct. Anal.,***231**(2006), 438--457. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
A. E. Litvak, "On the dual form of "Low M* -estimate"
in the quasi-convex case,"
*Positivity,***8**(2004), 401--406. PDF, PS. -
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. PDF, PS. -
Y. Gordon, A. E. Litvak, M. Meyer, A. Pajor,
"John's decomposition in the general case and applications,"
*J. of Diff. Geometry,***68**(2004), 99--119. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. -
A. E. Litvak, V. D. Milman,
"Euclidean sections of direct sums of normed spaces,"
*Can. Math. Bull.,***46**(2003), 242--251. PDF, PS. -
Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Geometry of spaces between zonoids and polytopes,"
*Bull. Sci. Math.,***126**(2002), 733--762. PDF, PS. -
Y. Gordon, A. E. Litvak, C. Schuett, E. Werner,
"Orlicz Norms of Sequences of Random Variables,"
*Ann. Probab.,***30**(2002), 1833--1853. PDF, PS. -
A. E. Litvak, P. Mankiewicz, N. Tomczak-Jaegermann,
"Randomized Isomorphic Dvoretzky Theorem,"
*C.R. Acad. Sci. Paris, Ser 1, Math.,***335**(2002), 345--350. PDF, PS. -
N. J. Kalton, A. E. Litvak,
"A remark on quotients of finite-dimensional quasi-normed spaces,"
*Houston Journal of Math.,***28**(2002), 585--597. PDF, PS. -
E. D. Gluskin, A. E. Litvak,
"On the asymmetry constant of a body with few vertices,"
*Geometriae Dedicate,***90**(2002), 45--48. PDF, PS. -
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. PDF, PS. -
A. E. Litvak,
"Kahane-Khinchin's inequality for the quasi-norms,"
*Can. Math. Bull.,***43**(2000), 368--379. PDF, PS. -
A. E. Litvak, N. Tomczak-Jaegermann,
"Random aspects of high-dimensional convex bodies,"
*GAFA, Lecture Notes in Math.,***1745**, 169--190, Springer-Verlag, 2000. PDF, PS. -
O. Guedon, A. E. Litvak,
"Euclidean projections of p-convex body,"
*GAFA, Lecture Notes in Math.,***1745**, 95--108, Springer-Verlag, 2000. PDF, PS. -
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. PDF, PS. - 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. PDF, PS. -
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. PDF, PS. -
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. PDF, PS. - A. E. Litvak, V. D. Milman, G. Schechtman,
"Averages of norms and quasi-norms,"
*Math. Ann.,***312**(1998), 95--124. PDF, PS. - 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. PDF, PS. -
A. E. Litvak,
"Properties of the operator of discrete integrations and some
applications,"
*Vestnik St. Petersburg Univ., Math.,***25**(1992), 28--30. PDF, PS.