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.