Publications
- M. Rudelson , A characterization of 2--trivial
Banach
spaces with an unconditional basis, Zap. Nauchn. Sem. LOMI 157
(1987), 76--87, Russian; English
translation in: Journal of
Soviet
Math., 44, no. 6, 800-808.
- M. Rudelson, Estimates
of the weak distance between finite--dimensional Banach spaces,
Israel J. of Math. 89(1995), 189--204.
- M. Rudelson, Approximate
John's decompositions, Operator Theory: Advances and
Applications 77(1995), 245--249.
- M. Avellaneda, A. V. Cherkaev, L. V. Gibiansky, G. W.
Milton,
M. Rudelson, A
complete
characterization of the possible bulk and shearmoduli of planar
polycrystals,
J. Mech. Phys. Solids,44(1996) 1179--1218.
- M. Rudelson, Contact
points
of convex bodies, Israel J. of Math. 101 (1997),
93-124.
- M. Rudelson, Almost
orthogonal
submatrices of an orthogonal matrix, Israel J. of Math. 111
(1999), 143-155.
- M. Rudelson, Random
vectors
in the isotropic position, J. of Functional Analysis,164
(1999) no. 1, 60-72.
- M. Rudelson, Sections
of
the difference body, Discrete and Comput. Geom. 23 (2000),
137-146.
- M. Rudelson, Distances
between non--symmetric convex bodies and the $MM^*$
estimate,
Positivity 4 (2000), no. 2, 161--178.
- A. A. Giannopoulos, V. D. Milman and M. Rudelson, Convex
bodies with minimal mean width, Geometric aspects of functional
analysis,
81--93, Lecture Notes in Math., 1745, Springer,
Berlin,
2001.
- M. Rudelson, R. Vershynin, Embeddings
of Levy families into Banach spaces, Geom. Funct. Anal.
12 (2002), no. 1, 183--198.
- M. Rudelson, Extremal distances between
sections
of convex bodies,
Geom. Funct. Anal. 14 (2004), no.
5,
1063--1088.
- M. Rudelson, R. Vershynin, Combinatorics
of random processes and
sections of convex bodies, Ann. of Math. (2)
164 (2006), no. 2, 603--648.
- A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and
geometry of random
polytopes, Adv. Math. 195
(2005), no. 2,
491--523.
- A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R.
Vershynin, Random Euclidean embeddings in
spaces of bounded volume ratio, Compt. Rendus Math. de
L'Academie des Sciences, Paris, Ser. 1 339 (2004), 33-38.
- S. Mendelson, A. Pajor, M. Rudelson, On the geometry of {-1,1} polytopes,
Discrete Comput. Geom. 34 (2005), no.
3, 365--379.
- 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.
- M. Rudelson, R. Vershynin, Geometric
approach to error correcting codes and reconstruction of signals,
Int. Math. Res. Not. 2005, no. 64,
4019--4041.
- M. Rudelson, R. Vershynin, Sampling from large matrices: an
approach through geometric functional analysis, J. ACM
54 (2007), no. 4, Art. 21, 19 pp.
- O. Guedon, M. Rudelson, L_p
moments of random vectors via majorizing measures, Adv. Math.
208 (2007), no. 2, 798--823.
- M. Rudelson, Invertibility of
random matrices: norm of the inverse, Annals of Mathematics
168 (2008), 575--600.
- E. Candes, M. Rudelson, T. Tao, R. Vershynin, Error correction via linear programming,
FOCS 2005 (46th Annual Symposium on Foundations of Computer Science).
- M. Rudelson, Lower
estimates for the singular values of random matrices,
Compt. Rendus Math. de
L'Academie des Sciences 342 (2006), no. 4,
247--252.
- M.Rudelson, R.Vershynin, On
sparse reconstruction from Fourier and Gaussian measurements, Comm.
Pure Appl. Math. 61 (2008), no. 8, 1025--1045.
- M.Rudelson, R.Vershynin, Sparse
reconstruction by convex relaxation: Fourier
and Gaussian measurements, CISS
2006 (40th Annual Conference on Information Sciences and Systems)
(an abridged version of the previous paper)
- M.Rudelson, R.Vershynin, The
Littlewood-Offord problem and invertibility of random matrices,
Adv. Math. 218 (2008), no. 2, 600--633.
- M.Rudelson, R.Vershynin,
The
smallest singular value of a rectangular random matrix, Comm. Pure
Appl. Math. 62 (2009), no. 12, 1707--1739.
- M. Rudelson, R. Vershynin, Non-asymptotic
theory of random
matrices: extreme singular values, Proceedings of the International
Congress of Mathematicians, Hyderabad, India, 2010.
- S. Kasiviswanathan, M. Rudelson, A. Smith, J. Ullmann, The price of privately releasing contingency
tables and the spectra of random matrices with correlated rows,
STOC 2010 (42nd ACM Symposium on Theory of Computing).
- M. Rudelson, Row products
of random matrices, Advances in Math., 231 (2012), no.6, 3199-3231.
- M. Rudelson, S. Zhou, Reconstruction
from anisotropic random measurements, IEEE Trans. Inform. Theory 59 (2013), no. 6, 3434-3447.
- S. Kasiviswanathan, M. Rudelson, A. Smith, The power of linear reconstruction attacks, SODA 2012 (ACM-SIAM Symposium on discrete algorithms).
- M. Rudelson, R. Vershynin, Invertibility of random matrices: unitary and orthogonal perturbations, J. Amer. Math. Soc. 27 (2014), no. 2, 293-338.
- A.Litvak, M. Rudelson, N. Tomczak-Jaegermann, Approximation by projections of polytopes with few facets, Israel J. Math. 203 (2014), no. 1, 141-160.
- M. Rudelson, Lecture notes on non-aymptotic random matrix theory, Modern Aspects of Random Matrix Theory -- AMS Proceedings of Symposia in Applied Mathematics - AMS, 2014, p. 83-121.
- M. Rudelson, O. Zeitouni, Singular values of Gaussian matrices and permanent estimators, Random Structures Algorithms 48 (2016), no. 1, 183-212.
- M. Rudelson, R. Vershynin, Hanson-Wright inequality and sub-gaussian concentration, Electronic Communications in Probability 18 (2013), 1-9.
- M. Rudelson, R. Vershynin, Delocalization of eigenvectors of random matrices with independent entries, Duke Math. J. 164 (2015), no. 13, 2507-2538.
- M. Rudelson, R. Vershynin, Small ball probabilities for linear images of high dimensional distributions, IMRN 2015, no. 19, 9594-9617.
- M. Rudelson, A. Samorodnitsky, O. Zeitouni, Hafnians, perfect matchings and Gaussian matrices, Ann. Probab. 44 (2016), no. 4, 2858-2888.
- M. Rudelson, On the complexity of the set of unconditional convex bodies, Discrete Comput. Geom. 55 (2016), no. 1, 185--202.
- M. Rudelson, R. Vershynin, No-gaps delocalization for general random matrices, Geom. Funct. Anal. 26 (2016), no. 6, 1716-1776.
- A. Basak, M. Rudelson, Invertibility of sparse non-hermitian matrices, Adv. Math. 310 (2017), 426-483.
- M. Rudelson, Delocalization of eigenvectors of random matrices. , IAS/Park City Mathematics Series, vol. 26 (2019), 303--340.
- A. Basak, M. Rudelson, The circular law for sparse non-Hermitian matrices, Ann. Probab. 47 (2019), no. 4, 2359--2416.
- S. Kasiviswanathan, M. Rudelson, Restricted eigenvalue from stable rank with applications to sparse linear regression, COLT 2018 (31 Annual Conference on Learning Theory).
- M. Rudelson, K. Tikhomirov, The sparse circular law under minimal assumptions, Geom. Funct. Anal. 29 (2019), no. 2, 561-637.
- A. Basak, M. Rudelson, Sharp transition of the invertibility of the adjacency matrices of random graphs, Probab. Theory Related Fields 180 (2021), no. 1-2, 233-308.
- H. Huang, M. Rudelson, Size of nodal domains of the eigenvectors of a G(n,p) graph, Random Structures Algorithms 57 (2020), no. 2, 393-438.
- H. Koenig, M. Rudelson, On the volume of non-central sections of a cube, Adv. Math. 360 (2020), 106929, 30 pp.
- A. Barvinok, M. Rudelson, When a system of real quadratic equations has a solution, Adv. Math. 403 (2022),108391, 38 pp.
- C. Mao, M. Rudelson, K. Tikhomirov, Exact matching of random graphs with constant
correlationn, submitted.
- A. Barvinok, M. Rudelson, A
quick estimate for the volume of a polyhedron, to appear in Israel
J. of Math.
- X. Dong, M. Rudelson, Approximately Hadamard matrices and Riesz bases in random frames, submitted.