On the construction of particle distributions with specified single and pair densities

We discuss necessary conditions for the existence of a probability distribution on particle configurations in d-dimensions, i.e., a point process, compatible with a specified density ρ and radial distribution function g(r). In d = 1 we give necessary and sufficient criteria on ρg(r) for the existence of such a point process of renewal (Markov) type. We prove that these conditions are satisfied for the case g(r) = 0, r D, if and only if ρD ≤ e-1:  the maximum density obtainable from diluting a Poisson process. We then describe briefly necessary and sufficient conditions, valid in every dimension, for ρg(r) to specify a determinantal point process for which all n-particle densities,ρn(r1,...,rn), are given explicitly as determinants. We give several examples.

• Publication year

  2004

• Venue

  Journal of Physical Chemistry B

• Publication date

  2004-05-21

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1021/JP047793MarXiv cond-mat/0405519
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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