Translation invariant realizability problem on the d-dimensional lattice : an explicit construction

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2016
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Caglioti, Emanuele
Kuna, Tobias
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Electronic Communications in Probability. 2016, 21, 45. eISSN 1083-589X. Available under: doi: 10.1214/16-ECP4620
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We consider a particular instance of the truncated realizability problem on the d-dimensional lattice. Namely, given two functions ρ1(i) and ρ2(i,j) non-negative and symmetric on Zd, we ask whether they are the first two correlation functions of a translation invariant point process. We provide an explicit construction of such a realizing process for any d ≥ 2 when the radial distribution has a specific form. We also derive from this construction a lower bound for the maximal realizable density and compare it with the already known lower bounds.

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ISO 690CAGLIOTI, Emanuele, Maria INFUSINO, Tobias KUNA, 2016. Translation invariant realizability problem on the d-dimensional lattice : an explicit construction. In: Electronic Communications in Probability. 2016, 21, 45. eISSN 1083-589X. Available under: doi: 10.1214/16-ECP4620
BibTex
@article{Caglioti2016Trans-33285,
  year={2016},
  doi={10.1214/16-ECP4620},
  title={Translation invariant realizability problem on the d-dimensional lattice : an explicit construction},
  volume={21},
  journal={Electronic Communications in Probability},
  author={Caglioti, Emanuele and Infusino, Maria and Kuna, Tobias},
  note={Article Number: 45}
}
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