The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  • Adamczak, Radosław; Guédon, Olivier; Litvak, Alexander; Pajor, Alain; Tomczak-Jaegermann, Nicole. Smallest singular value of random matrices with independent columns. C. R. Math. Acad. Sci. Paris 346 (2008), no. 15-16, 853--856. MR2441920
  • Chevet, S. Séries de variables aléatoires gaussiennes à valeurs dans $E\hat \otimes _{\varepsilon }F$. Application aux produits d'espaces de Wiener abstraits. (French) Séminaire sur la Géométrie des Espaces de Banach (1977–1978), Exp. No. 19, 15 pp., École Polytech., Palaiseau, 1978. MR0520217
  • Edelman, Alan. Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Appl. 9 (1988), no. 4, 543--560. MR0964668
  • Gordon, Yehoram; Litvak, Alexander; Schütt, Carsten; Werner, Elisabeth. Orlicz norms of sequences of random variables. Ann. Probab. 30 (2002), no. 4, 1833--1853. MR1944007
  • Latała, Rafał. Some estimates of norms of random matrices. Proc. Amer. Math. Soc. 133 (2005), no. 5, 1273--1282 (electronic). MR2111932
  • Ledoux, Michel. The concentration of measure phenomenon. Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9 MR1849347
  • Litvak, A. E.; Pajor, A.; Rudelson, M.; Tomczak-Jaegermann, N. Smallest singular value of random matrices and geometry of random polytopes. Adv. Math. 195 (2005), no. 2, 491--523. MR2146352
  • Pisier, Gilles. The volume of convex bodies and Banach space geometry. Cambridge Tracts in Mathematics, 94. Cambridge University Press, Cambridge, 1989. xvi+250 pp. ISBN: 0-521-36465-5; 0-521-66635-X MR1036275
  • Rudelson, Mark; Vershynin, Roman. Smallest singular value of a random rectangular matrix. Comm. Pure Appl. Math. 62 (2009), no. 12, 1707--1739. MR2569075
  • Rudelson, Mark; Vershynin, Roman. The least singular value of a random square matrix is $O(n^ {-1/2})$. C. R. Math. Acad. Sci. Paris 346 (2008), no. 15-16, 893--896. MR2441928
  • Ruskai, Mary Beth; Werner, Elisabeth. Study of a class of regularizations of $1/\vert X\vert $ using Gaussian integrals. SIAM J. Math. Anal. 32 (2000), no. 2, 435--463 (electronic). MR1781466
  • Seginer, Yoav. The expected norm of random matrices. Combin. Probab. Comput. 9 (2000), no. 2, 149--166. MR1762786
  • Schütt, Carsten. On the Banach-Mazur distance of finite-dimensional symmetric Banach spaces and the hypergeometric distribution. Studia Math. 72 (1982), no. 2, 109--129. MR0665413
  • Szarek, Stanisław J. Condition numbers of random matrices. J. Complexity 7 (1991), no. 2, 131--149. MR1108773

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.