The Annals of Probability

Measures with zeros in the inverse of their moment matrix

J. William Helton, Jean B. Lasserre, and Mihai Putinar

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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.

Article information

Ann. Probab., Volume 36, Number 4 (2008), 1453-1471.

First available in Project Euclid: 29 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45]
Secondary: 52A

Moment matrix orthogonal polynomials


Helton, J. William; Lasserre, Jean B.; Putinar, Mihai. Measures with zeros in the inverse of their moment matrix. Ann. Probab. 36 (2008), no. 4, 1453--1471. doi:10.1214/07-AOP365.

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