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July 2008 Measures with zeros in the inverse of their moment matrix
J. William Helton, Jean B. Lasserre, Mihai Putinar
Ann. Probab. 36(4): 1453-1471 (July 2008). DOI: 10.1214/07-AOP365


We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure μ has zeros in some prescribed entries. We describe precisely which pattern of these zeroes corresponds to independence, namely, the measure having a product structure. A more refined finding is that the key factor forcing a zero entry in this inverse matrix is a certain conditional triangularity property of the orthogonal polynomials associated with μ.


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J. William Helton. Jean B. Lasserre. Mihai Putinar. "Measures with zeros in the inverse of their moment matrix." Ann. Probab. 36 (4) 1453 - 1471, July 2008.


Published: July 2008
First available in Project Euclid: 29 July 2008

zbMATH: 1169.15005
MathSciNet: MR2435855
Digital Object Identifier: 10.1214/07-AOP365

Primary: 52A20
Secondary: 52A

Keywords: Moment matrix , orthogonal polynomials

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 4 • July 2008
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