Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-30T20:15:25.140Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Relation Between the Gaussian Orthogonal Ensemble and Reflections, or a Self-Adjoint Version of the Marcus–Pisier Inequality

Published online by Cambridge University Press:  20 November 2018

Roy Wagner
Roy Wagner*
Affiliation:
Computer Science Department, Academic College of Tel-Aviv-Yaffo, Israel e-mail: rwagner@mta.ac.il
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove a self-adjoint analogue of the Marcus–Pisier inequality, comparing the expected value of convex functionals on random reflection matrices and on elements of the Gaussian orthogonal (or unitary) ensemble.

Keywords

15A5246B0946L54
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 2 , 01 June 2006 , pp. 313 - 320
Copyright
Copyright © Canadian Mathematical Society 2006

References

[A] Arnold, L., On the asymptotic distribution of the eigenvalues of random matrices. J. Math. Anal. Appl. 20(1967), 262–268.Google Scholar
[BG] Benyamini, Y. and Gordon, Y., Random factorizations of operators between Banach spaces. J. Anal. Math. 39(1981), 45–74.Google Scholar
[BM] Bourgain, J. and Milman, V., Distances between normed spaces, their subspaces and quotient spaces. Integral Equations Operator Theory 9(1986), 31–46.Google Scholar
[BY] Bai, Z. D. and Yin, Y. K., Necessary and sufficient conditions for the almost sure convergence of the largest eigenvalue of a Wigner matrix. Ann. Probab. 16(1988), 1729–1741.Google Scholar
[DMT] Davis, W., Milman, V. and Tomczak-Jaegermann, N., The distance between certain n-dimensional spaces. Israel J. Math. 39(1981), 1–15.Google Scholar
[DS] Davidson, K. R. and Szarek, S. J., Local operator theory, random matrices and Banach spaces. In: Handbook of the geometry of Banach spaces, volume I, (eds., Johnson, W. B. and Lindenstrauss, J.), North-Holland, 2001, 317–366.Google Scholar
[G] Geman, S., A limit theorem for the norm of random matrices. Ann. Probab. 8(1980), 252–261.Google Scholar
[HT] Haagerup, U. and Thorbjørnsen, S., Random matrices with complex Gaussian entires. Exposition. Math. 21(2003), 293–337.Google Scholar
[MP] Marcus, M. B. and Pisier, G., Random Fourier Series with Applications to Harmonic Analysis. Center for Statistics and Probability, Northwestern University 44, 1980.Google Scholar
[PL] Pastur, L. and Lejay, A., Matrices aléatoires: statistique asymptotique des valeurs propres. In: Séminaire de probabilités 23, Lecture Notes in Math. 1801, Springer, 2003, 135–164.Google Scholar
[S1] Szarek, S. J., The volume of separable states is super-doubly-exponentially small. preprint, http://arxiv.org/abs/quant-ph/0310061.Google Scholar
[S2] Szarek, S. J., Condition numbers of random matrices. J. Complexity (2) 7(1991), 131–149.Google Scholar
[T] Tomczak-Jaegermann, N., Banach–Mazur Distance and finite-dimensional Operator Ideals. Pitman Monographs and Surveys in Pure and Applied Math. 38, 1989.Google Scholar