Papers by year

Papers by Alexander Litvak

all selected by coauthors

by year: 1992-1999    2000-2002    2003-2005 2006-2008 2009-2011 2012-2014 2015-2017 2018-2020 2021-2023 2024-2026


2024-2026

D. Janz, A. E. Litvak, C. Szepesvari, "Ensemble sampling for linear bandits: small ensembles suffice," submitted. PDF.

D. Galicer, A. E. Litvak, M. Merzbacher, D. Pinasco, "On the volume ratio of projections of convex bodies," J. of Funct. Anal., 286 (2024), 110242. PDF.

2021-2023

A. E. Litvak, G. V. Livshyts, "New bounds on the minimal dispersion," J. of Complexity, 72 (2022), 101648. PDF.

A. E. Litvak, K. Tikhomirov, "Singularity of sparse Bernoulli matrices," Duke Math. Journal, 171 (2022), 1135--1233. PDF.

A. E. Litvak, D. Zaporozhets, "Generalized Busemann inequality," Zapiski Nauchnykh Seminarov POMI, 505 (2021), 162--171; English translation: Journal of Math. Sciences, to appear. PDF.

A. E. Litvak, "A remark on the minimal dispersion," Commun. Contemp. Math., 23/6 (2021), 2050060. 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.

2018-2020

A. E. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, "Small ball probability for the condition number of random matrices," GAFA, Lecture Notes in Math., 2266 (2020), 125--137. PDF.

O. Guedon, A. E. Litvak, K. Tatarko, "Random polytopes obtained by matrices with heavy tailed entries," Commun. Contemp. Math., 22 (2020), 1950027. 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, "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.

2015-2017

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, 238 (2019), 523--529. 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.

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.

2012-2014

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.

2009-2011

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.

2006-2008

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.

2003-2005

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.