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Probabilistic estimates for tensor products of random vectors


Authors: David Alonso-Gutiérrez, Markus Passenbrunner and Joscha Prochno
Journal: Proc. Amer. Math. Soc. 144 (2016), 2133-2148
MSC (2010): Primary 46B09, 46B07, 46B28, 46B45
DOI: https://doi.org/10.1090/proc/12883
Published electronically: October 5, 2015
MathSciNet review: 3460173
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Abstract: We prove some probabilistic estimates for tensor products of random vectors, generalizing results that were obtained by Gordon, Litvak, Schütt, and Werner [Ann. Probab., 30(4):1833-1853, 2002], and Prochno and Riemer [Houst. J. Math., 39(4):1301-1311, 2013]. As an application we obtain embeddings of certain matrix spaces into $ L_1$.


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Additional Information

David Alonso-Gutiérrez
Affiliation: Departament de Matemàtiques, Universitat Jaume I, Campus de Riu Sec, E12071 Castelló de la Plana, Spain
Email: alonsod@uji.es

Markus Passenbrunner
Affiliation: Institute of Analysis, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria
Email: markus.passenbrunner@jku.at

Joscha Prochno
Affiliation: Institute of Analysis, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria
Address at time of publication: Department of Mathematics, University of Hull, Robert Blackburn Building, Hull, HU6 7RX, United Kingdom
Email: j.prochno@hull.ac.uk

DOI: https://doi.org/10.1090/proc/12883
Keywords: Orlicz function, Orlicz norm, random vector, tensor product
Received by editor(s): April 29, 2014
Received by editor(s) in revised form: June 10, 2015
Published electronically: October 5, 2015
Additional Notes: The first author was partially supported by Instituto de Matemáticas y Aplicaciones de Castellón, MINECO project MTM2013-42105-P, and BANCAJA project P1-1B2014-35
The second author was supported by the Austrian Science Fund, FWF P23987 and P27723
The third author was supported by the Austrian Science Fund, FWFM 1628000.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society