Helton, J. William; Lasserre, Jean B.; Putinar, Mihai Measures with zeros in the inverse of their moment matrix. (English) Zbl 1169.15005 Ann. Probab. 36, No. 4, 1453-1471 (2008). The paper focuses on the multivariate truncated moment matrix, \(M_d\), consisting of moments of a measure \(\mu\) up to an order determined by \(d\). First, the authors describe precisely which pattern of zeros of \(M_d^{-1}\) corresponds to independence, namely, the measure \(\mu\) having a product type structure. Next, the authors turn to the study of a particular entry of \(M_d^{-1}\) being zero. They find that the key factor is a certain conditional triangularity property of the orthogonal polynomials up to degree \(2d\), associated with the measure \(\mu\). Reviewer: Hu Yong-Jian (Beijing) Cited in 5 Documents MSC: 15B51 Stochastic matrices 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis Keywords:moment matrix; orthogonal polynomials × Cite Format Result Cite Review PDF Full Text: DOI arXiv References: [1] Dunkl, C. F. and Xu, Y. (2001). Orthogonal Polynomials of Several Variables . Cambridge Univ. Press. · Zbl 0964.33001 [2] Berg, C. (2008). Fibonacci numbers and orthogonal polynomials. J. Comput. Appl. Math. · Zbl 1231.33009 [3] Cripps, E., Carter, C. and Kohn, R. (2003). Variable selection and covariance selection in multiregression models. Technical Report #2003-14, Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC. [4] Magnus, W. and Oberhettinger, F. (1949). Formulas and Theorems for the Functions of Mathematical Physics . Chelsea reprint, New York. · Zbl 0039.07202 [5] Reznick, B. (1992). Sums of Even Powers of Real Linear Forms . Amer. Math. Soc., Providence, RI. · Zbl 0762.11019 [6] Suetin, P. K. (1988). Orthogonal Polynomials in Two Variables . (In Russian). Nauka, Moscow. · Zbl 0658.33004 [7] Whittaker, J. (1990). Graphical Models in Applied Mathematical Analysis . Wiley, New York. · Zbl 0732.62056 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.