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.

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

Kuna T.
2016

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/175992
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