标题： 粒子分布的构建具有指定的单体和对密度 显示英文标题

标题： On the Construction of Particle Distributions with Specified Single and Pair Densities

摘要： 我们讨论在$d$维空间中粒子构型的概率分布存在的必要条件，即与指定密度$\rho$和径向分布函数$g({\bf r})$相容的点过程。在$d=1$中，我们给出关于$\rho g({\bf r})$的必要且充分条件，以存在此类重置（马尔可夫）类型的点过程。 我们证明，当且仅当$\rho D \leq e^{-1}$时，这些条件对于情况$g(r) = 0, r < D$和$g(r) = 1, r > D$成立：从稀释泊松过程可获得的最大密度。 然后我们简要描述在每个维度中有效的必要和充分条件，以使$\rho g(r)$指定一个确定点过程，其中所有$n$粒子密度，$\rho_n({\bf r}_1, ..., {\bf r}_n)$，作为行列式明确给出。 我们给出几个示例。 显示英文摘要

摘要： 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 $\rho$ and radial distribution function $g({\bf r})$. In $d=1$ we give necessary and sufficient criteria on $\rho g({\bf r})$ 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 $\rho D \leq e^{-1}$: the maximum density obtainable from diluting a Poisson process. We then describe briefly necessary and sufficient conditions, valid in every dimension, for $\rho g(r)$ to specify a determinantal point process for which all $n$-particle densities, $\rho_n({\bf r}_1, ..., {\bf r}_n)$, are given explicitly as determinants. We give several examples.