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

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

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CAGLIOTI, Emanuele, Maria INFUSINO, Tobias KUNA, 2016. Translation invariant realizability problem on the d-dimensional lattice : an explicit construction. In: Electronic Communications in Probability. 21, 45. eISSN 1083-589X

@article{Caglioti2016Trans-33285, title={Translation invariant realizability problem on the d-dimensional lattice : an explicit construction}, year={2016}, doi={10.1214/16-ECP4620}, volume={21}, journal={Electronic Communications in Probability}, author={Caglioti, Emanuele and Infusino, Maria and Kuna, Tobias}, note={Article Number: 45} }

2017-08-17T12:57:12Z Infusino, Maria Caglioti, Emanuele 2016 Infusino, Maria Caglioti, Emanuele Kuna, Tobias Translation invariant realizability problem on the d-dimensional lattice : an explicit construction eng Kuna, Tobias We consider a particular instance of the truncated realizability problem on the d-dimensional lattice. Namely, given two functions ρ<sub>1</sub>(i) and ρ<sub>2</sub>(i,j) non-negative and symmetric on Z<sup>d</sup>, 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. 2017-08-17T12:57:12Z

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