Stochastic dominance of nearest-neighbor distances in PLM-PPP and PSP-PPP

Let $n>1$ and consider the distance from a typical general vehicle to its $n$th-nearest neighbor in the PLM-PPP and in the PSP-PPP, with Rayleigh-distributed half-lengths. Nearest-neighbor distance dominance conjecture. The distance in the PLM-PPP stochastically dominates the corresponding distance in the PSP-PPP. This conjecture extends the observed nearest-neighbor comparison to the $n$th-nearest neighbor; the paper presents it as an inference from numerical results, and no proof or resolution is provided.