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On Bobkov's approximate de Finetti representation via approximation of permanents of complex rectangular matrices


Author: Bero Roos
Journal: Proc. Amer. Math. Soc. 143 (2015), 1785-1796
MSC (2010): Primary 60G09, 62E17, 15A45
DOI: https://doi.org/10.1090/S0002-9939-2014-12429-4
Published electronically: December 4, 2014
MathSciNet review: 3314090
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Abstract: Bobkov (J. Theoret. Probab. 18(2) (2005) 399-412) investigated an approximate de Finetti representation for probability measures, on product measurable spaces, which are symmetric under permutations of coordinates. One of the main results of that paper was an explicit approximation bound for permanents of complex rectangular matrices, which was shown by a somewhat complicated induction argument. In this paper, we indicate how to avoid the induction argument using an (asymptotic) expansion. Our approach makes it possible to give new explicit higher order approximation bounds for such permanents and in turn for the probability measures mentioned above.


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Additional Information

Bero Roos
Affiliation: FB IV – Department of Mathematics, University of Trier, 54286 Trier, Germany
Email: bero.roos@uni-trier.de

DOI: https://doi.org/10.1090/S0002-9939-2014-12429-4
Keywords: de Finetti representation, permanent, Hadamard type inequality
Received by editor(s): March 13, 2012
Received by editor(s) in revised form: September 20, 2013
Published electronically: December 4, 2014
Communicated by: Walter Craig
Article copyright: © Copyright 2014 American Mathematical Society