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

Kuna, T., Caglioti, E. and Infusino, M. (2016) Translation invariant realizability problem on the d-dimensional lattice: an explicit construction. Electronic Communications in Probability, 21. 45. ISSN 1083-589X doi: 10.1214/16-ECP4620

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/65902
Identification Number/DOI	10.1214/16-ECP4620
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Institute of Mathematical Statistics and Bernoulli Society
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