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.
Titolo: | Translation invariant realizability problem on the d-dimensional lattice: An explicit construction | |
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Data di pubblicazione: | 2016 | |
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Handle: | http://hdl.handle.net/11697/175992 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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File | Descrizione | Tipologia | Licenza | |
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1510.02954.pdf | Documento in Pre-print | ![]() | Open Access Visualizza/Apri | |
16-ECP4620.pdf | Documento in Versione Editoriale | ![]() | Open Access Visualizza/Apri |
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