Selected papers
- A. E. Litvak, K. Tikhomirov,
"Singularity of sparse Bernoulli matrices,"
Duke Math. Journal,
171 (2022), 1135--1233.
PDF.
- A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"Circular law for sparse random regular digraphs,"
Journal of the European Mathematical Society,
23 (2021), 467--501.
PDF.
- A. E. Litvak, A. Lytova, K. Tikhomirov, N. Tomczak-Jaegermann, P. Youssef,
"Structure of eigenvectors of random regular digraphs,"
Trans. Amer. Math. Soc.,
371 (2019), 8097--8172.
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,
173 (2019), 1301--1347.
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,
"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.
- 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.
- 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, 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.
- 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,
"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,
"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,
"Entropy extension," Funct. Anal. Appl., 40 (2006),
298--303. 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.
- 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.
- 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, N. Tomczak-Jaegermann,
"Random aspects of high-dimensional convex bodies," GAFA, Lecture
Notes in Math., 1745, 169--190,
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, G. Schechtman,
"Averages of norms and quasi-norms," Math. Ann., 312 (1998),
95--124. PDF, PS.