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Theoretical
Mathematics
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Applied
Mathematics
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Some papers are
listed under multiple categories.
Geometric Functional Analysis
- M. Rudelson, R. Vershynin, The least singular value of a random square matrix is O(n^{-1/2}), submitted.
- M.
Rudelson, R.
Vershynin, The smallest singular
value of a random rectangular matrix, submitted. Commentary.
Slides.
- M. Rudelson, R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices, Advances in Mathematics 218 (2008), 600--633. Commentary. Slides.
- B. Klartag, R.Vershynin, Small
ball probability and Dvoretzky theorem,
Israel Journal of
Mathematics 157 (2007), 193--207. Commentary
- R.Vershynin, Isoperimetry
of waists and local versus global asymptotic convex geometries
(with an appendix by M.Rudelson and R.Vershynin), Duke Mathematical Journal 131
(2006), 1--16 Commentary
- M. Rudelson, R.Vershynin, Combinatorics of
random processes and sections
of convex bodies, Annals of Mathematics 164 (2006),
603--648. Commentary
and Introductory
Notes
- R. Vershynin, Integer
cells in convex sets, Advances in Mathematics 197 (2005),
248--273
- A. Litvak, A. Pajor,
M. Rudelson, N. Tomczak-Jaegermann,
R. Vershynin, Euclidean
embeddings in spaces of finite volume ratio via random matrices, Journal
für die Reine
und Angewandte Mathematik
589 (2005), 1--19
- A. Litvak, A. Pajor,
M. Rudelson, N. Tomczak-Jaegermann,
R. Vershynin, Random
Euclidean embeddings in spaces of bounded volume ratio, Comptes rendus
de l'Académie des sciences - Mathématique 339 (2004), 33--38
- S. Mendelson, R.Vershynin, Remarks
on the geometry of
coordinate projections in R^n,
Israel Journal of Mathematics 140 (2004), 203--220
- S. Mendelson, R.Vershynin, Entropy
and the combinatorial dimension, Inventiones
Mathematicae 152 (2003), 37--55
- G. Schechtman, N. Tomczak-Jaegermann,
R. Vershynin, Maximal
l_p^n-structures in spaces with extremal parameters, Geometric
aspects of functional analysis, 223--240, Lecture Notes in Mathematics, 1807,
Springer, Berlin, 2003
- M. Rudelson, R. Vershynin, Embedding
Levy families into Banach spaces,
Geometric and Functional
Analysis 12 (2002), 183--198
- R. Vershynin, John's
decompositions: selecting a large part, Israel Journal of
Mathematics 122 (2001), 253--277
- R. Vershynin, Subsequences of frames, Studia Mathematica 145 (2001), 185--197
- N. Tomczak-Jaegermann,
R. Vershynin, Sizes
of projections of symmetric convex
bodies, unpublished
- R.Vershynin, On
large random almost Euclidean bases, Acta Mathematica
Universitatis Comenianae
69 (2000), no. 2, 137--144
- R.Vershynin, Absolutely
representing systems, uniform smoothness and type, Questionae Mathematica
23 (2000), no. 1, 87--98
- R. Vershynin, On constructions of strong and uniformly minimal
M-bases in Banach spaces, Arch.
Math. (
- R. Vershynin,
Embedding of operator ranges
and the reflexivity of Banach spaces
(Russian), Ukrainian Math. Journal
51 (1999), no. 2, 293--296
- R. Vershynin, On
1+epsilon_n-bounded M-bases (Russian), Russian Math. (Iz. VUZ) 43 (1999), no. 4, 22--25
- R. Vershynin, On representing and absolutely representing
systems in Banach spaces (Russian), Mat.
Fiz. Anal. Geom. 5 (1998), 3--14
- V. Kadets, R. Vershynin, The selection problem for bases with brackets and for strong M-bases, Rendiconti Istituto Lombardo Sez. A 131 (1997), 169--177
Operator Theory
- M. Rudelson, R. Vershynin, Sampling
from large
matrices: an approach through geometric functional analysis, Journal of the ACM (2007),
Art. 21, 19 pp. Commentary.
- R. Vershynin, Random
sets of isomorphism of linear operators on Hilbert space, IMS
Lecture Notes -- Monograph Series, High Dimensional Probability,
Vol. 51 (2006), 148--154. Commentary
- M. Rudelson, R.Vershynin, Combinatorics of random processes and sections of convex bodies, Annals of Mathematics 164 (2006), 603--648. Commentary and Introductory Notes
- R. Vershynin, John's decompositions: selecting a large part, Israel Journal of Mathematics 122 (2001), 253--277
- R. Vershynin, Embedding of operator ranges and the reflexivity of Banach spaces (Russian), Ukrainian Math. Journal 51 (1999), no. 2, 293--296
- M. Rudelson, R. Vershynin, The least singular value of a random square matrix is O(n^{-1/2}), submitted.
- M.
Rudelson, R.
Vershynin, The smallest singular
value of a random rectangular matrix, submitted. Commentary. Slides.
- M. Rudelson, R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices, Advances in Mathematics 218 (2008), 600--633. Commentary. Slides.
- B. Klartag, R.Vershynin, Small ball probability and Dvoretzky theorem, Israel Journal of Mathematics 157 (2007), 193--207. Commentary
- M. Rudelson, R.Vershynin, Combinatorics of random processes and sections of convex bodies, Annals of Mathematics 164 (2006), 603--648. Commentary and Introductory Notes
- A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, Euclidean embeddings in spaces of finite volume ratio via random matrices, Journal für die Reine und Angewandte Mathematik 589 (2005), 1--19
- A. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, R. Vershynin, Random Euclidean embeddings in spaces of bounded volume ratio, Comptes rendus de l'Académie des sciences - Mathématique 339 (2004), 33--38
- S. Mendelson, R.Vershynin, Entropy and the combinatorial dimension, Inventiones Mathematicae 152 (2003), 37--55
Geometric Combinatorics
- M. Rudelson, R.Vershynin, Combinatorics of random processes and sections of convex bodies, Annals of Mathematics 164 (2006), 603--648. Commentary and Introductory Notes
- R. Vershynin, Integer cells in convex sets, Advances in Mathematics 197 (2005), 248--273
- S. Mendelson, R.Vershynin, Entropy and the combinatorial dimension, Inventiones Mathematicae 152 (2003), 37--55
- S. Mendelson, R.Vershynin, Entropy, Combinatorial dimensions and Random Averages, in: COLT 2002 (15th Annual Conference on Computational Learning Theory), edited by J. Kivinen and R. Sloan, Springer 2002, p. 14--28
Numerical Analysis
- M. Rudelson, R. Vershynin, The least singular value of a random square matrix is O(n^{-1/2}), submitted.
- M.
Rudelson, R.
Vershynin, The smallest singular
value of a random rectangular matrix, submitted. Commentary.
Slides.
- M. Rudelson, R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices, Advances in Mathematics 218 (2008), 600--633. Commentary. Slides.
- R. Vershynin, Some problems in asymptotic convex geometry and random matrices motivated by numerical algorithms. In: Banach Spaces and their applications in analysis, de Gruyter, 2007, pp. 209--218
- M. Rudelson, R. Vershynin, Sampling from large matrices: an approach through geometric functional analysis, Journal of the ACM (2007), Art. 21, 19 pp. Commentary
- T. Strohmer,
R. Vershynin, A
randomized solver for linear
systems with exponential convergence, RANDOM 2006 (10th
International Workshop on Randomization and Computation), Springer
Lecture Notes in Computer Science 4110, 499--507. Commentary
Journal version: A randomized Kaczmarz algorithm with exponential convergence, Journal of Fourier Analysis and Applications, to appear - R. Vershynin, Beyond
Hirsch Conjecture: walks on random polytopes
and smoothed complexity of the simplex method, FOCS 2006 (47th
Annual Symposium on Foundations of Computer Science), 133--142. Commentary
Journal version: Beyond Hirsch Conjecture: walks on random polytopes and smoothed complexity of the simplex method, submitted
Computational Harmonic Analysis, Compressed Sensing and Coding
- D. Needell, R.
Vershynin, Signal recovery from
incomplete and inaccurate measurements via Regularized Orthogonal
Matching Pursuit, sumbitted. Commentary.
Conference version: Greedy signal recovery and uncertainty principles, Computational Imaging VI, IS&T/SPIE 19th Annual Symposium, 2008. Proc. SPIE Vol. 6814, 68140J. - D. Needell, R. Vershynin, Uniform Uncertainty Principle and signal recovery via Regularized Orthogonal Matching Pursuit, Foundations of Computational Mathematics, DOI: 10.1007/s10208-008-9031-3. Commentary
- Yu. Lyubarskii, R. Vershynin, Uncertainty principles and vector quantization, submitted. Commentary. Slides.
- A. Gilbert, M. Strauss, J. Tropp, R. Vershynin, One sketch for all: fast algorithms for compressed sensing, STOC 2007 (39th ACM Symposium on Theory of Computing), to appear
- A.
Gilbert, M. Strauss, J. Tropp, R. Vershynin, Algorithmic
linear dimension
reduction in the ell-1 norm for sparse vectors, submitted.
Commentary
Conference version: Algorithmic Linear Dimension Reduction in the L1 Norm for Sparse Vectors, Allerton 2006 (44th Annual Allerton Conference on Communication, Control, and Computing), invited paper - M. Rudelson, R.Vershynin, Sparse
reconstruction by convex relaxation:
Fourier and Gaussian measurements, CISS 2006 (40th Annual
Conference on Information Sciences and Systems), invited paper. Commentary
Journal version: On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, to appear. Commentary - M. Rudelson, R.Vershynin, Geometric
approach to error correcting codes and
reconstruction of signals, International Mathematical Research
Notices 64 (2005), 4019--4041 Commentary
Conference version: E. Candes, M. Rudelson, T. Tao, R. Vershynin, Error correction via Linear Programming, FOCS 2005 (46th Annual Symposium on Foundations of Computer Science), 295--308 - R.Vershynin, Frame expansions with erasures: an approach through the non-commutative operator theory, Applied and Computational Harmonic Analysis 18 (2005), 167--176 Commentary
Statistical Learning Theory
- M. Rudelson, R.Vershynin, Combinatorics of random processes and sections of convex bodies, Annals of Mathematics 164 (2006), 603--648. Commentary and Introductory Notes
- S. Mendelson, R.Vershynin, Entropy and the combinatorial dimension, Inventiones Mathematicae 152 (2003), 37--55
- S. Mendelson, R.Vershynin, Entropy, Combinatorial dimensions and Random Averages, in: COLT 2002 (15th Annual Conference on Computational Learning Theory), edited by J. Kivinen and R. Sloan, Springer 2002, p. 14--28