Measures with zeros in the inverse of their moment matrix

Details Measures with zeros in the inverse of their moment matrix Measures with zeros in the inverse of their moment matrix

2007-02-12

arxiv.org/abs/math/0702314v2

Annals of Probability 2008, Vol. 36, No. 4, 1453-1471

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/07-AOP365 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/07-AOP365

We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure $\mu$ 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 $\mu$.

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