On the Construction of Particle Distributions with Specified Single and Pair Densities
| dc.creator | Costin, O. | |
| dc.creator | Lebowitz, J. L. | |
| dc.date | 2004-05-21 | |
| dc.date.accessioned | 2026-07-07T02:58:17Z | |
| dc.date.available | 2026-07-07T02:58:17Z | |
| dc.description | We discuss necessary conditions for the existence of probability distribution on particle configurations in $d$-dimensions i.e. a point process, compatible with a specified density $ρ$ and radial distribution function $g({\bf r})$. In $d=1$ we give necessary and sufficient criteria on $ρg({\bf r})$ for the existence of such a point process of renewal (Markov) type. We prove that these conditions are satisfied for the case $g(r) = 0, r < D$ and $g(r) = 1, r > D$, if and only if $ρD \leq e^{-1}$: 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, $ρ_n({\bf r}_1, ..., {\bf r}_n)$, are given explicitly as determinants. We give several examples. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0405519 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0405519 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24024 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Mathematical Physics | |
| dc.title | On the Construction of Particle Distributions with Specified Single and Pair Densities | |
| dc.type | text |