## The Annals of Probability

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

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

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

#### Abstract

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

**Source**

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

**Dates**

First available in Project Euclid: 29 July 2008

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1217360975

**Digital Object Identifier**

doi:10.1214/07-AOP365

**Mathematical Reviews number (MathSciNet)**

MR2435855

**Zentralblatt MATH identifier**

1169.15005

**Subjects**

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

Secondary: 52A

**Keywords**

Moment matrix orthogonal polynomials

#### Citation

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. https://projecteuclid.org/euclid.aop/1217360975