Problem: Given an arrangement of spheres of varying radii in a fixed domain , I am trying to simulate an arrangement of spheres in a domain of arbitrary size having the same statistics. The radii of the spheres are spatially correlated and the correlation function of the sphere radii is homogeneous

A naive approach I am thinking of is to generate a Gaussian random field representing the radii of the spheres on a background grid as a covariate. Then randomly insert spheres into the domain with their radii taken from this random field, rejecting them if they overlap with existing spheres. This process would go on until the same spheres-to-domain volume ratio is reached as the sample arrangement.

I would be grateful if someone could suggest a better or alternative way of going about this problem.


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