The realizability problem as infinite dimensional moment problem
The problem of describing a point process from its low order correlation functions is well-known in statistical mechanics as realizability problem, but naturally occurs also in several other areas dealing with the analysis of complex systems. In this talk we give an interpretation of this problem as an infinite dimensional version of the classical moment problem, which has recently proved to be an effective approach towards new advances in this area. In particular, we illustrate how the realizability problem can be seen as a special instance of moment problem for random measures for which we obtained new solvability conditions exploiting the structure of the support of the representing measure (see https://doi.org/10.1016/j.jmaa.2019.123551).
Area: CS57 - Statistical Mechanics and applications (Tobias Kuna)
Keywords: realizability problem, moment problem
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