Chevet type inequality and norms of submatrices

• Autorzy: Radosław Adamczak , Rafał Latała , Alexander E. Litvak , Alain Pajor , Nicole Tomczak-Jaegermann
• Języki publikacji: EN

Abstrakty

EN

We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of the expectation of the supremum of "symmetric exponential" processes, compared to the Gaussian ones in the Chevet inequality. This is used to give a sharp upper estimate for a quantity $Γ_{k,m}$ that controls uniformly the Euclidean operator norm of the submatrices with k rows and m columns of an isotropic log-concave unconditional random matrix. We apply these estimates to give a sharp bound for the restricted isometry constant of a random matrix with independent log-concave unconditional rows. We also show that our Chevet type inequality does not extend to general isotropic log-concave random matrices.

Kategorie tematyczne

• 52A23: Asymptotic theory of convex bodies
• 94B75: Applications of the theory of convex sets and geometry of numbers (covering radius, etc.)
• 46B06: Asymptotic theory of Banach spaces
• 60E15: Inequalities; stochastic orderings
• 15B52: Random matrices
• 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 1
• Strony: 35-56

Daty

wydano

2012

Twórcy

autor

Radosław Adamczak

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Rafał Latała

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Alexander E. Litvak

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

autor

Alain Pajor

• Équipe d'Analyse et Mathématiques Appliquées, Université Paris-Est, 5, boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallée, Cedex 2, France

autor

Nicole Tomczak-Jaegermann

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

Identyfikatory

DOI

10.4064/sm210-1-3