Seminario Dottorato: Moment Problems and Spin Correlation Matrices

Thursday 5 April 2012 - Neeraja Sahasrabudhe

ARGOMENTI: Seminars Ph.D. Program

Thursday 5 April 2012 h. 11:30, room 2BC30
Neeraja Sahasrabudhe (Dip. Mat.)
"Moment Problems and Spin Correlation Matrices"

Moment problems are about realizability of a given pair correlation function or covariances (or higher moments), namely whether a probability distribution is determined by its moments. That is, given $m_0,m_1,...inR$, one wants to find a probability measure $mu$ such that $int_{-infty}^{+infty} x^k dmu(x) = m_k$ for $k=0,1,...$. If the probability measure is determined uniquely by the given set of moments the problem is called a determinate moment problem. Generalized moment problems of this kind have been widely studied, mainly in the theoretical Engineering community, for continuous random variables (particularly in case of point processes).
In this talk, I'll discuss moment problems in general, giving examples of some determinate and indeterminate moment problems. We will also look at some specific moment problems and the necessary and sufficient conditions for realizability. I'll also talk about my work which is about a moment problem on a system of spin random variables. I will discuss about the necessary and sufficient conditions for a correlation matrix of order $ngeq 2$ to be the correlation matrix of spin variables in the classical sense and finally try to give an algorithm to explicitly compute the probability measure that realizes the given correlations.

Rif. int. C. Marastoni, T. Vargiolu

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