Identifying interacting pairs of sites in infinite range Ising models

Details Identifying interacting pairs of sites in infinite range Ising models Identifying interacting pairs of sites in infinite range Ising models

2010-06-02

arxiv.org/abs/1006.0272v2

Mathematics

Statistics Theory

Few typos corrected

Scientific paper

We consider Ising models (pairwise interaction Gibbs probability measures) in $\Z^d$ with an infinite range potential. We address the problem of identifying pairs of interacting sites from a finite sample of independent realisations of the Ising model. The sample contains only the values assigned by the Ising model to a finite set of sites in $\Z^d$. Our main result is an upperbound for the probability with our estimator to misidentify the pairs of interacting sites in this finite set.

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