- B. Farrell, R. Vershynin,
Smoothed analysis of symmetric random matrices with continuous distributuions,
submitted. [arXiv:1212.3531].
Hagelstein's weak triangle inequality for weak L1 norm used in this paper is discussed here:
- R. Vershynin,
Weak triangle inequalities for weak L1 norm,
not intended for publication (2012).
- A. Ai, A. Lapanowski, Y. Plan and R. Vershynin,
One-bit compressed sensing with non-Gaussian measurements,
Linear Algebra and Applications, to appear.
[arXiv:1208.6279].
- M. Rudelson, R. Vershynin, Invertibility of random matrices: unitary and orthogonal perturbations, Journal of the AMS, to appear.
[arXiv:1202.1212].
- Y. Plan, R. Vershynin, Robust 1-bit compressed sensing and sparse logistic regression:
a convex programming approach,
IEEE Transactions on Information Theory 59 (2013), 482--494. [arXiv:1202.1212].
- Y. Plan, R. Vershynin, Dimension reduction by random hyperplane tessellations, submitted.
[arXiv:1111.4452].
- Y. Plan, R. Vershynin, One-bit compressed sensing by linear programming,
Communications on Pure and Applied Mathematics, to appear.
[arXiv:1109.4299].
See also 1BitCompressiveSensing page at Rice.
- R. Vershynin, A tribute to Nigel J. Kalton (1946-2010),
Peter Casazza (coordinating editor), Alexander Pelczynski, Joe Diestel, Roman Vershynin, Gilles Godefroy,
Notices of the AMS 59 (7), August 2012, 942--951.
- N. Srivastava, R. Vershynin,
Covariance estimation for distributions with 2+epsilon moments,
Annals of Probability, to appear.
- R. Vershynin,
A simple decoupling inequality in probability theory,
not intended for publication (2011).
- R. Vershynin,
Invertibility of symmetric random matrices,
Random Structures and Algorithms, to appear. [arXiv:1102.0300].
- E. Levina, R. Vershynin,
Partial estimation of covariance matrices,
Probability Theory and Related Fields 153 (2012), 405--419.
[arXiv:1008.1716].
- R. Vershynin,
How close is the sample covariance matrix
to the actual covariance matrix?
Journal of Theoretical Probability 25 (2012), 655--686.
[arXiv:1004.3484].
- R. Vershynin,
Approximating the moments of marginals of high dimensional distributions,
Annals of Probability 39 (2011), 1591--1606.
- R. Vershynin,
Spectral norm of products of random and deterministic matrices,
Probability Theory and Related Fields 150 (2011), 471--509. DOI: 10.1007/s00440-010-0281-z.
Commentary.
-
Yu. Lyubarskii, R. Vershynin,
Uncertainty principles and vector quantization,
IEEE Transactions on Information Theory 56 (2010), 3491--3501.
Commentary.
Slides.
- T. Strohmer, R. Vershynin,
Comments on the randomized Kaczmarz method,
Journal of Fourier Analysis and Applications 15 (2009), 437--440.
Commentary.
- M. Rudelson, R. Vershynin,
Smallest singular value of a random rectangular matrix,
Communications on Pure and Applied Mathematics 62 (2009), 1707--1739.
Commentary.
Slides.
-
D. Needell, R. Vershynin,
Signal recovery from incomplete and inaccurate measurements
via Regularized Orthogonal Matching Pursuit,
IEEE Journal of Selected Topics in Signal Processing 4 (2010), 310--316.
Commentary.
A conference version:
D. Needell, R. Vershynin,
Signal recovery from incomplete and inaccurate measurements via ROMP,
SAMPTA'09 (8th international conference on Sampling Theory and Applications), 2009.
One more conference version:
D. Needell, R. Vershynin,
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 9 (2009), 317--334.
Commentary.
- M. Rudelson, R. Vershynin,
The least singular value of a random square matrix is O(n^{-1/2}),
Comptes rendus de l'Académie des sciences - Mathématique 346 (2008), 893--896.
Commentary.
- M. Rudelson, R. Vershynin,
The Littlewood-Offord Problem and invertibility of random matrices,
Advances in Mathematics 218 (2008), 600--633.
Commentary.
- M. Rudelson, R. Vershynin,
Sampling from large matrices: an approach through geometric functional analysis,
Journal of the ACM (2007), Art. 21, 19 pp.
Commentary.
- A. Gilbert, M. Strauss, J. Tropp, R. Vershynin,
One sketch for all: fast algorithms for compressed sensing,
STOC'07--Proceedings of the 39th Annual ACM Symposium on Theory of Computing,
237--246, ACM, New York, 2007.
Complete version of the paper.
- B. Klartag, R. Vershynin,
Small ball probability and Dvoretzky theorem,
Israel Journal of Mathematics 157 (2007), 193--207.
Commentary.
- T. Strohmer, R. Vershynin,
A randomized solver for linear systems with exponential convergence,
Approximation, randomization and combinatorial optimization, 499--507,
Lecture Notes in Comput. Sci., 4110,
Springer, Berlin, 2006.
Commentary
Journal version:
A randomized Kaczmarz algorithm with exponential convergence,
Journal of Fourier Analysis and Applications 15 (2009), 262--278.
- 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,
SIAM Journal on Computing 39 (2009), 646--678 (Invited paper).
-
A. Gilbert, M. Strauss, J. Tropp, R. Vershynin,
Algorithmic linear dimension reduction in the ell-1 norm for sparse vectors,
unpublished.
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'06 (40th Annual Conference on Information Sciences and Systems),
2006, 207--212
Commentary.
Journal version:
On sparse reconstruction from Fourier and Gaussian measurements,
Communications on Pure and Applied Mathematics 61 (2008), 1025-1045.
Commentary.
- R. Vershynin,
Random sets of isomorphism of linear operators on Hilbert space,
High dimensional probability, 148--154,
IMS Lecture Notes Monogr. Ser., 51, Inst. Math. Statist.,
Beachwood, OH, 2006.
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.
Introductory Notes.
- 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),
668--681.
- R. Vershynin,
Frame expansions with erasures: an approach through the non-commutative
operator theory,
Applied and Computational Harmonic Analysis 18 (2005), 167--176
Commentary.
- R. Vershynin,
Integer cells in convex sets,
Advances in Mathematics 197 (2005), 248--273.
- P. G. Casazza, O. Christensen, A. M. Lindner, R. Vershynin,
Frames and the Feichtinger conjecture,
Proceedings of the AMS 133 (2005), 1025--1033.
- 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.
- 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.
- N. Tomczak-Jaegermann, R. Vershynin,
Sizes of projections of symmetric convex bodies,
unpublished (2001).
- R. Vershynin,
Subsequences of frames,
Studia Mathematica 145 (2001), 185--197.
- 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), 87--98.
- R. Vershynin,
On constructions of strong and uniformly minimal M-bases in Banach spaces,
Archiv der Mathematik (Basel) 74 (2000), 50--60.
- R. Vershynin,
Imbedding of the images of operators and reflexivity of Banach spaces (Russian),
Ukrainian Mathematical Journal 51 (1999), 293--296.
- R. Vershynin,
On 1+epsilon_n-bounded M-bases (Russian),
Russian Mathematics (Izvestiya VUZ. Matematika) 43 (1999), 22--25.
- R. Vershynin,
On representing and absolutely representing systems in Banach spaces (Russian),
Matematicheskaya Fizika, Analiz, Geometriya 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.
